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Design of lattice structures with controlled anisotropy
Abstract
Recent advances in additive manufacturing make it possible to fabricate periodic lattice structures with complex configurations. However, a proper design strategy to achieve lattice structures with controlled anisotropy is still unavailable. There is an urgent need to fill this knowledge gap in order to develop mechanical metamaterials with prescribed properties. Here we propose two different methodologies to design lattice structures with controlled anisotropy. As examples, we created two new families of lattice structures with isotropic elasticity and cubic symmetric geometry. The findings of this work provide simple and effective strategies for exploring lightweight metamaterials with desired mechanical properties.
... Isotropic materials exhibit the same mechanical properties in all directions, making them highly desirable for achieving uniform load distribution and structural stability. To quantify the variance for the stiffness in different directions of cubic structures, the Zener ratio A is used and defined as [51,52]: ...
... A compression load case to calculate the stiffness components C 11 , C 12 which relate to normal stresses and a shear load case for the calculation of C 44 which specifies the shear modulus for a structure as shown in Figure 10a. This methodology has been previously employed for the precise calculation of the polar stiffness map of structure, leading to a close correlation between theoretical and experimental results [52]. The elastic stiffness components can be calculated by dividing the average strain (ε) through the average stress (σ) [61][62][63]: ...
... Further information on the applied boundary conditions and FEA models can be found in the SI and elsewhere [46,52,63]. Utilizing the simulations and effective stiffness properties, the cost function values for isotropy and auxeticity can be determined. ...
Recent advancements in manufacturing, finite element analysis (FEA), and optimization techniques have expanded the design possibilities for metamaterials, including isotropic and auxetic structures, known for applications like energy absorption due to their unique deformation mechanism and consistent behavior under varying loads. However, achieving simultaneous control of multiple properties, such as optimal isotropic and auxetic characteristics, remains challenging. This paper introduces a systematic design approach that combines modeling, FEA, neural networks, and optimization to create targeted mechanical behavior in metamaterials. Through strategically arranging 8 distinct neither isotropic nor auxetic unit cell states, the stiffness tensor in a 5 × 5 × 5 cubic symmetric lattice structure is controlled. Employing the NSGA-II genetic algorithm and automated modeling, we yield metamaterial lattice structures possessing both, desired isotropic and auxetic properties. Multiphoton lithography fabrication and experimental characterization of the optimized metamaterial highlights a practical real-world use and confirms close correlation between theoretical and experimental data.
... Lumpe and Stankovic [8] investigated numerous pentamode structures showing the importance of crystallographic symmetries on the mechanical properties of the structure. Xu et al [9] proposed two different methodologies to design lattice structures with controlled anisotropy. Huang et al. [10] introduced a new class of pentamode metamaterial with centrosymmetry, showing better mechanical characteristics. ...
... Thus, for the vertical stiffness Eqs. (8) and (9) can be suggested for the equivalent diameter for SPMs and TPMs respectively: ...
... d eq = 0.09×D + 0.91×d (9) Similarities can be found between the response to the horizontal and the vertical loading. Once again, the thicker specimens seem to be strongly influenced by the variation of the diameters of the beams. ...
Metameterials have unique properties, which are mostly attributed to their geometrical configuration. Pentamodes, a subcategory of metamaterials, exhibit an almost zero shear elastic modulus while maintaining high compression stiffness, offering a behavior similar to that of a liquid, suggesting the potential application of pentamodes in seismic isolation. In this paper a real-life bridge bearing, composed of repetitive layers of pentamode unit cells in the horizontal and vertical axes is studied. The lattices are modelled using beam finite elements with an equivalent uniform diameter to ensuring a stiffness equal to that of the bi-cone rod. The importance of the chosen equivalent diameter is shown, as the assumption of an average diameter of the bi-cone may lead to significant discrepancies between the calculated stiffnesses. For small bi-cone diameters difference, and slender formulations, the error could grow up to 15% for the horizontal stiffness and up to 200% for vertical. For thick formulations the average diameter overestimates the horizontal stiffness by 3 times and the vertical by 4. These discrepancies grow exponentially as the bi-cone diameters difference increases. An elastoplastic material is selected. The bearing supporting the superstructure is subjected to a constant vertical weight load and a horizontal shear base load, due to seismic excitation. Under vertical loading plastic hinges are created in all the rods of the cell and bearing. However, under shear loading plastic hinges are rather initially created in the lowest nodes of the cell and the bearing.
... Structured materials with unprecedented tunable properties have been increasingly developed in recent years and have found applications in robotics, [1,2] electronics, [3] energy harvesting systems, [4,5] biomedical engineering, [6] aerospace engineering, [7,8] structural engineering, [9] etc. [10][11][12] These materials, which are referred to as metamaterials, are engineered to exhibit properties that are derived from their architecture, rather than constituent materials. [13,14] Negative swelling ratio, [10] negative thermal expansion coefficient, [15] negative Poisson's ratio, [16] negative moduli, [17] anisotropic behavior, [18,19] reversible nonlinear deformability, [20,21] programmability, [22,23] and shape memorability [24] are some of the obtained mechanical properties. ...
... Structures used as modules for the development of modular metamaterials vary from rotating rigid shapes, [28][29][30][31] the wide range of honeycomb designs, [32][33][34] and re-entrant structures [35][36][37] to horseshoe-shaped structures, [10] foldable obelisk-like units, [25] bioinspired double-layer hinges, [38] helical structures, [39] and many other different designs. [2,19,22,40,41] The aim of this study is to investigate the potential of preprogrammable compliant double-spiral structures, which have been recently introduced by our team, when used as the modules of a metastructure. Adjustable design, multiple degrees of freedom, high extensibility, and reversible nonlinear deformability are properties of the double-spirals that make them particularly interesting for the development of deformable structures. ...
... We could tune all these features by changing the design variables of the double-spirals and controlling the structural stiffness in each direction. These characteristics can be a great advantage to many engineering structures, such as mechanical hinges [46,47] biomedical implants, [19] asymmetric casts and splints, [48] flexible body armors, [49] and loadbearing yet collision-resistant kites. [50] Programmed shape change in response to mechanical loads is another interesting property of the metastructures. ...
Metamaterials with adjustable, sometimes unusual properties offer advantages over conventional materials with predefined mechanical properties in many technological applications. A group of metamaterials, called modular metamaterials or metastructures, are developed through the arrangement of multiple, mostly similar building blocks. These modular structures can be assembled using prefabricated modules and reconfigured to promote efficiency and functionality. Herein, a novel modular metastructure is developed by taking advantage of the high compliance of preprogrammable double-spirals. First, the mechanical behavior of a four-module metastructure under tension, compression, rotation, and sliding is simulated using the finite-element method. Then, 3D printing and mechanical testing are used to illustrate the tunable anisotropic and asymmetric behavior of the spiral-based metastructures in practice. The results show the simple reconfiguration of the presented metastructure toward the desired functions. The mechanical behavior of single double-spirals and the characteristics that can be achieved through their combinations make our modular metastructure suitable for various applications in robotics, aerospace, and medical engineering.
... Through additive manufacturing (AM), patient-specific or complex three-dimensional objects, such as lattice structures, can be created cost-effectively by adding materials layer by layer. Unlike traditional manufacturing methods, which involve removing material from a solid block or bringing the parts together to make up a whole, additive manufacturing creates an object from scratch and is well-suited for the production of lattice structures [8][9][10]. ...
... Previous studies have investigated various lattice structures that can be used for prosthetics. The focus was mainly on lattice shapes, load directions, strain distributions, the creation of porous devices by material extraction, and the study of stiffness matrices [9,12,[14][15][16]. Liu et al. investigated the effect of several different stem types and different auxetic designs on stress shielding and reported that although the results varied with stem type and Gruen zones, auxetic stems caused less stress shielding than their solid counterparts [17]. ...
Artificial hip joints are used to replace damaged or diseased natural joints. When the stress that is typically applied to the bone changes because the implant and bone are different in stiffness, a phenomenon known as stress shielding occurs. Stress shielding can lead to bone weakening through reduced density and aseptic loosening in the long term. Studies are ongoing to overcome this phenomenon through geometric design, the use of materials with a low modulus of elasticity, or latticed implants. In this study, the effect of lightening the hip prosthesis with lattice structures on stress shielding is investigated using finite element simulation. The femoral stem of a solid hip prosthesis was lightweighted, with a re-entrant honeycomb auxetic cellular lattice structure, and structural analysis was performed. Two different lattice orientations were used, and it was observed that the stress distribution was more homogeneous in both orientations. In these femoral stems, which can be easily produced using additive manufacturing methods, a volume reduction of up to 16% was achieved. The stress transmitted to the bone increased by more than 36%, depending on the orientation, which is a promising result for reducing the stress shield effect.
... To design the target structure with controllable anisotropy, some strategies have been proposed and validated. The first strategy is the assembly design of different unit cell types at the same or different scales [21][22][23], and even the isotropic trusslattices could be harvested [22]. Another strategy is the replacement of truss-lattices with shell-lattices by using the bending-energy based function, and more detailed discussions could be found in [16,24,25]. ...
... However, it should be noted that, despite the anisotropy could be controlled, they all larger than 1, indicating that an isotopic solid could not be obtained in this way. An alternative way is to integrate different types of architectures into one configuration [22,23], which would be investigated in our further study. ...
Truss-lattices have wide application prospects in various important fields owing to their superior mechanical properties and energy absorption characteristics. In this paper, two typical truss-lattice materials (i.e. bending-dominated body-centred cubic (BCC) and stretch-dominated Octet architectures) were designed with enhanced mechanical properties and tunable anisotropy. The elastoplastic properties and large strain response were both investigated numerically and experimentally. Numerical results showed that a relative larger stiffness characteristic could be harvested when the shape parameter was chosen between 0.2 and 0.3, and the anisotropy degree could also be controlled through the shape parameter. Large strain multi-cell simulations also demonstrated the enhanced plastic properties and energy absorption characteristics of the designed architectures. The numerical findings were then confirmed through the uniaxial compression experiments on the 316L stainless steel truss-lattices specimens fabricated by the Selective Laser Melting (SLM) process. This study would broaden the design idea for the 3D truss-lattices with enhanced mechanical performance and tunable anisotropy, which may of great potential in engineering applications.
... Lattice-like materials such as cellular, porous, reticulated systems with regular structure are a class of functional-structural materials whose physical and mechanical overall properties result from a unique combination of tailored microstructure and material properties of its constituents [1][2][3]. Actually, the ever-growing possibilities of innovative three-dimensional printing and additive manufacturing technologies, make it possible nowadays to design and produce on a large scale truss, beam-like or other periodic reticulated lattice structures with non-conventional and remarkable static and dynamic properties [4][5][6][7]. To obtain unusual elastic properties such as auxeticity, chirality and/or noncentrosymmetry, various microstructural topologies can be considered [8][9][10][11][12]. ...
... Once all the discrete variables in Eqs. (6) have been mapped in the k-space, it is possible to introduce the continuous field variables, satisfying the relations v R pk, tq . " F´1pkqvpk, tq, ...
Lattice-like materials featuring periodic planar tessellation of regular rigid blocks connected by linear elastic interfaces and chiral or achiral properties are considered. The chirality results from a uniform rotation of the blocks with respect to their centroidal joining line and leads to interesting auxetic and dispersive acoustic behaviors. The governing equations of the discrete Lagrangian model are properly manipulated via the novel enhanced continualization scheme in such a way to obtain equivalent non-local integral and gradient-type higher-order continua. Based on the formal Taylor series expansion of the integral kernels or the corresponding pseudo-differential functions accounting for shift operators and proper pseudo-differential downscaling laws, the proposed enhanced continualization technique allows formulating homogeneous non-local continuum models of increasing orders, analytically featured by characteristic non-local constitutive and inertial terms. The enhanced continualization shows thermodynamic consistency in the definition of the overall non-local constitutive tensors, as well as qualitative agreement and quantitative convergent matching of the actual complex frequency band structure. The theoretical findings are successfully verified though the study of wave dispersion and attenuation properties as referred to a representative tetrachiral geometry.
... Many design applications [17][18][19][20][21] have been limited to a small catalog of ad-hoc lattices (e.g., kagome, octet, and octahedron [22][23][24][25][26][27][28], which have been identified through a combination of intuition and trial-and-error over the years. While the catalog-based search space can be enriched by tuning geometric features 29 or base material properties 19 , it is strongly limited in topological tunability and fails to exploit the full range of achievable designs and hence of achievable effective metamaterial properties. Many truss optimization solutions have adopted heuristic search strategies to find optimal structures by iteratively adjusting the active beams and/or nodes in the design domain, according to mechanics-based criteria [30][31][32][33] . ...
The rise of machine learning has fueled the discovery of new materials and, especially, metamaterials—truss lattices being their most prominent class. While their tailorable properties have been explored extensively, the design of truss-based metamaterials has remained highly limited and often heuristic, due to the vast, discrete design space and the lack of a comprehensive parameterization. We here present a graph-based deep learning generative framework, which combines a variational autoencoder and a property predictor, to construct a reduced, continuous latent representation covering an enormous range of trusses. This unified latent space allows for the fast generation of new designs through simple operations (e.g., traversing the latent space or interpolating between structures). We further demonstrate an optimization framework for the inverse design of trusses with customized mechanical properties in both the linear and nonlinear regimes, including designs exhibiting exceptionally stiff, auxetic, pentamode-like, and tailored nonlinear behaviors. This generative model can predict manufacturable (and counter-intuitive) designs with extreme target properties beyond the training domain.
... However, inclined struts are commonly seen in various strut-based lattice designs. The three main reasons are (i) to enhance the diversity of lattice topology otherwise all lattice designs will comprise horizontal and vertical struts, (ii) to help mitigate anisotropic properties [6,7] lattice topologies consisting of only horizontal and vertical struts often exhibit prominent anisotropy, and (iii) to facilitate the use of the Maxwell criterion (m) by increasing the number of struts to make > 0 (stretching-dominated) this allows control of the lattice deformation mechanism according to the Gibson-Ashby model [8]. However, from a PBF-AM perspective, dealing with inclined struts is almost unavoidable. ...
Additively manufactured metal lattices or metamaterials are often used in the form of conformal lattices. A prerequisite for realizing the design potential of these conformal lattice components is to ensure that each submillimetre to millimetre scale constituent strut achieves a uniform cross-sectional profile along its strut axis. However, in the design space of conformal lattices, the inclination angles of the constituent struts can vary considerably, even when simple cubic unit cells are used. This poses a challenge in selecting the diameter of each inclined strut for powder bed fusion (PBF) additive manufacturing (AM), because the manufacturable diameter of a strut is closely related to its inclination angle. On the other hand, while choosing a thick strut diameter could ensure a uniform cross-sectional profile for an inclined strut, this often results in an excessive lattice relative density, thereby hindering lightweight design. Through the design and detailed characterization of a complex Ti-6Al-4V conformal lattice, we show that the challenge of choosing the strut diameter versus strut inclination angle in a complex conformal lattice structure can be well answered by using a strut additive continuity model recently developed by the authors.
... Not surprising, these observations attribute to the proportion of the structures. A high β corresponds to a SC tube dominated structure where most of the materials are axially aligned in the [1 0 0] direction while a low β corresponds to an FCC plate dominated structure where stronger localization is observed in the [1 0 0] direction [33]. At a transition stage, with β = 0.48, near-isotropic structures can be realized. ...
... They are a multidisciplinary research community encompassing structural analysis, materials science, mechanics, and engineering. As a result, research groups have aimed to design functionally graded material properties of composites to achieve improved physical and mechanical behaviors that cannot be obtained from conventional engineering materials [6][7][8][9]. ...
... Optimization-based approaches are usually referred to as topology optimization, which is also known as inverse homogenization methods [21,22]. Although these techniques have been extensively utilized in prior research [23][24][25][26][27][28], they pose a challenge in 3D lattice inverse design, primarily due to their computationally intensive nature. Additionally, the structures generated by these methods may not be easily manufacturable [18,22,29]. ...
This paper investigates the feasibility of data-driven methods in automating the engineering design process, specifically studying inverse design of cellular mechanical metamaterials. Traditional methods of designing cellular materials typically rely on trial and error or iterative optimization, which often leads to limited productivity and high computational costs. While data-driven approaches have been explored for the inverse design of cellular materials, many of these methods lack robustness and fail to consider the manufacturability of the generated structures. This study aims to develop an efficient inverse design methodology that accurately generates mechanical metamaterial while ensuring the manufacturability of predicted structures. To achieve this, we have created a comprehensive dataset that spans a broad range of mechanical properties by applying rotations to cubic structures synthesized from the nine cubic symmetries of cubic materials. We then employ a physics-guided neural network (PGNN) consisting of dual neural networks: a generator network, which serves as the inverse design tool, and a forward network, which acts as a physics-guided simulator. The goal is to generate desired anisotropic stiffness components with unit-cell design parameters. The results of our inverse model are examined with three distinct datasets and demonstrate high computational efficiency and prediction accuracy compared to conventional methods.
... Strut-based lattice structures are often chosen for their simplicity of design, but strut-based topologies have also been generated from topological optimization to maximize the efficiency of material distribution within the lattice structure (Xiao et al., 2018a;Xu et al., 2016). Alternative topologies to strut-based structures are lattice structures with unit cells based on triply periodic minimal surfaces (TPMS) such as the Schoen gyroid, Schwartz diamond and Neovius (Maconachie et al., 2019). ...
Graded lattice scaffolds based on rhombic dodecahedral (RD) elementary unit cell geometry were manufactured in 316L stainless steel (SS) by laser powder bed fusion (LPBF). Two different strategies based on varying strut thickness layer-by-layer in the building direction were adopted to obtain the graded scaffolds: a) decreasing strut size from core to edge to produce the dense-in (DI) structure and b) increasing strut size in the same direction to produce the dense-out (DO) structure. Both graded structures (DI and DO) were constructed with specular symmetry with respect to the central horizontal axis. Structural, mechanical, and biological characterizations were carried out to evaluate feasibility of designing appropriate biomechanical performances of graded scaffolds in the perspective of bone tissue regeneration. Results showed that mechanical behavior is governed by graded geometry, while printing parameters influence structural properties of the material such as density, textures, and crystallographic phases. The predominant failure mechanism in graded structures initiates in correspondence of thinner struts, due to high stress concentrations on strut junctions. Biological tests evidenced better proliferation of cells in the DO graded scaffold, which in turn exhibits mechanical properties close to cortical bone. The combined control of grading strategy, printing parameters and elementary unit cell geometry can enable implementing scaffolds with improved biomechanical performances for bone tissue regeneration.
... In recent studies, the triply periodic minimal surface (TPMS) lattice structures generated by implicit functions are attractive for industrial applications owing to their superior mechanical properties [15][16][17][18][19][20]. The anisotropic property of TPMS-based lattice structure is one of the significant characteristics [21][22][23][24] and the geometric feature is the key factor affecting the anisotropy performance [25]. To further enhance the mechanical properties of components in lightweight design application, it is worth investigating the anisotropic performance of the lattice structures [26]. ...
... Up till now, inclined struts have been commonly included in lattice design (Fig. 1). Their main roles may be summarized as follows: (i) to just enhance the diversity of lattice topology, (ii) to help mitigate the anisotropic properties of some lattice designs [113,114], and (iii) to facilitate the use of the Maxwell criterion by increasing the total strut number to make m > 0 so as to control the lattice deformation mechanism by the G-A model (for l /d > 5) [10]. One such example is octet-truss lattices (m > 0), but they are much weaker than cubic lattices of the same density [61,63]. ...
The Gibson-Ashby (G-A) model has been instrumental in the design of additively manufactured (AM-ed) metal lattice materials or mechanical metamaterials. The first part of this work reviews the proposition and formulation of the G-A model and emphasizes that the G-A model is only applicable to low-density lattice materials with strut length-to-diameter ratios greater than 5. The second part evaluates the applicability of the G-A model to AM-ed metal lattice materials and reveals the fundamental disconnections between them. The third part assesses the
deformation mechanisms of AM-ed metal lattices in relation to their strut length-to-diameter ratios and identifies
that AM-ed metal lattices deform by concurrent bending, stretching, and shear, rather than just stretching or
bending considered by the G-A model. Consequently, mechanical property models coupling stretching, bending and shear deformation mechanisms are developed for various lattice materials, which show high congruence with experimental data. The last part discusses new insights obtained from these remedies into the design of strong and stiff metal lattices. In particular, we recommend that the use of inclined struts be avoided.
... Engineering Structures xxx (xxxx) 116249 cluding grain boundaries, precipitates, and phases to obtain robust and damage-tolerant lattice structures [17]. Combination of FCC and BCC lattice was also reported to enhance plastic energy absorption [18] and promote controlled anisotropy [19]. Multi-morphology structures were made of two materials of different properties to also investigate the interplay of base material properties within the hybrid topology. ...
The fabrication freedom offered by additive manufacturing techniques is a unique asset to be exploited in the design of lightweight lattice structures. Adjusting topological and architectural features towards the design of multi-morphological lattice structures can offer a high potential towards obtaining fine-tuned mechanical response. Herein, to understand the role of unit cell topology and arrangement, various stacking and gradient strategies were implemented to modulate the overall mechanical response of the lattice structures under compression, using two Triply Periodical Minimal Surface (TPMS) unit cell designs. Experimental and numerical approaches were developed to reveal the deformation mechanism and failure modes and quantify stiffness, quasi-static uniaxial compressive strength, and energy absorption capacity of the structures. The topological arrangement of the selected unit cells was found to play a key role in defining the mechanical performance of the designed lattice structures. The obtained results demonstrated the high potential of various graded design elements for obtaining lattice structures with desired properties.
... Lattice structures, such as 3D-Kagome [1][2][3][4], eight-truss grid structure [5,6], bodycentered cubic (BCC) [7], body-centered cubic with Z-direction struts (BCCZ) [8], simple cubic (SC) [9] and face-centered cubic (FCC) lattices [10], have large strength to mass ratios, good energy absorption and highly efficient energy storage [11]. The development of 3D printing technology has greatly enriched the types of lattice structures that can be manufactured. ...
An analytical method to predict the elastic modulus of the sandwich body-centered cubic (BCC) lattice structure is presented on the basis of the assumption of a linearly changing elastic modulus. In the constrained region, the maximum of elastic modulus used the elastic moduli of the BCC lattice element with plate constraints and is calculated with Timoshenko beam theory, the minimum used without plate constraints. In the rest of the constrained region, a linear function along the thickness direction is proposed to calculate elastic modulus. The elastic modulus of the unconstrained region is constant and it is the same as the minimum of the constrained region. The elastic modulus of the whole sandwich BCC lattice structure can be calculated theoretically with the elastic modulus of the constrained and unconstrained regions and a single-layer slice integration method. Six kinds of sandwich BCC lattice structures with different geometric parameters are designed and made by resin 3D printing technology, and the elastic moduli are measured. By comparing the predictions of the elastic modulus using the proposed analytical method and existing method with experimental results, the errors between the results of the existing method and the experimental results varied from 10.3% to 24.7%, and the errors between the results of the proposed method and the experimental results varied from 1.6% to 7.4%, proving that the proposed method is more accurate than the existing methods.
... For the numerical implementation of homogenization, one component of the strain vector is set to unity, and the rest are set to zero as shown in Eq. (8) [39][40][41]. This will lead to a stress tensor and can be calculated from reaction forces at the corresponding surfaces. ...
Owing to its excellent mechanical properties, triply periodic minimum surfaces (TPMS) lattice structures have recently gained more interest in engineering applications. The superior properties of these structures make it easier to achieve engineering design goals such as strength and weight. However, technological advancements compel the designer to enhance the traditional TPMS design qualities. Hybridization of different lattice types emerges as a strong candidate for enhancing overall design performance. Therefore, a hybrid optimization scheme based on genetic algorithms (GA) and anisotropic homogenization-based topology optimization is considered to generate a functionally graded multi-morphology for a Messerschmitt–Bölkow–Blohm (MBB) beam design in this paper. The GA is performed to identify the best lattice morphology, including Diamond (D), Gyroid (G), I-WP, and Primitive (P), and their relative densities prior to topology optimization (TO). Once the best lattice morphology of the design domain is obtained via the GA, the homogenization-based topology optimization is applied to grade the multi-morphology lattice to improve the design performance further. The final step is the reconstruction of the graded multi-morphology using a novel blending algorithm. The reconstructed MBB beams are made of cobalt-chromium (CoCr) alloy and are then manufactured using the laser sintering method, direct metal laser melting (DMLM) technique. Destructive metallographic and non-destructive metrological techniques are utilized to assure manufacturing quality. An impact hammer test is conducted on the fabricated beams to validate and compare the proposed graded multi-morphology geometry with graded and uniform single lattice morphologies. Experimental results show that the stiffness of the graded multi-morphology structure designed by the proposed hybrid optimization is 4.5 % and 13.0 % higher than the graded form of D and P-type single lattice morphologies, respectively. Also, it is observed that the graded form single lattice morphologies deliver superior performance than their uniform encounters namely D and P-type lattice structures.
... Approximate isotropy Anisotropy is an important criterion for measuring the overall structural performance. The degree of anisotropy of MSLC can be quantified by the Zener index A. It can be calculated based on C M SLC [69] as follows: ...
Structural design with multi-family triply periodic minimal surfaces (TPMS) is a meaningful work that can combine the advantages of different types of TPMS. However, very few methods consider the influence of the blending of different TPMS on structural performance, and the manufacturability of final structure.
Therefore, this work proposes a method to design manufacturable microstructures with topology optimization (TO) based on spatially-varying TPMS. In our method, different types of TPMS are simultaneously considered in the optimization to maximize the performance of designed microstructure.
The geometric and mechanical properties of the unit cells generated with TPMS, that is minimal surface lattice cell (MSLC), are analyzed to obtain the performance of different types of TPMS. In the designed microstructure, MSLCs of different types are smoothly blended with an interpolation method.
To analyze the influence of deformed MSLCs on the performance of the final structure, the blending blocks are introduced to describe the connection cases between different types of MSLCs. The mechanical properties of deformed MSLCs are analyzed and applied in TO process to reduce the influence of deformed MSLCs on the performance of final structure.
The infill resolution of MSLC within a given design domain is determined according to the minimal printable wall thickness of MSLC and structural stiffness.
Both numerical and physical experimental results demonstrate the effectiveness of the proposed method.
... The Zener ratio is defined as Z = 2C 44 /(C 11 − C 12 ), and Z = 1 indicates an isotropic material behavior [55,56]. ...
... For example, Nguyen et al. regulated and optimized the position and orientation of the struts to improve the stiffness of the lattice under six loading conditions (XX, YY, ZZ, YZ, XY, XZ) [7]. Xu et al. proposed two design strategies regulating the anisotropy of the struts-based lattice by assembling different base units and adjusting the ratio of rod diameters, respectively [8]. In addition, Maxwell's principle provides clear guidance for designing high-stiffness strut-based lattices [9]. ...
Reliable extreme lightweight is the pursuit in many high-end manufacturing areas. Aided by additive manufacturing (AM), lattice material has become a promising candidate for lightweight optimization. Configuration of lattice units at the material level and the distribution of lattice units at the structure level are the two main research directions recently. This paper proposes a generative strategy for lattice infilling optimization using organic strut-based lattices. A sphere packing algorithm driven by von Mises stress fields determines the lattice distribution density. Two typical configurations, Voronoi polygons and Delaunay triangles, are adopted to constitute the frames, respectively. Based on finite element analysis, a simplified truss model is utilized to evaluate the lattice distribution in terms of mechanical properties. Optimization parameters, including node number, mapping gradient, and the range of varying circle size, are investigated through the genetic algorithm (GA). Multiple feasible solutions are obtained for further solidification modelling. To avoid the stress concentration, the organic strut-based lattice units are created by the iso-surface modelling method. The effectiveness of the proposed generative approach is illustrated through a classical 3-point bending beam. The stiffness of the optimized structure, verified through experimental testing, has increased 80% over the one using the traditional uniform body center cubic (BCC) lattice distribution.
... The lattice structure might give good characteristics, including a superior strength/weight ratio, good thermal properties, and acoustic shielding, making it perfect for high-profit industrial objectives such as aerospace [30]. The more important feature of lattice structures is the best structural efficiency per unit weight [31]. In [32] the pumping system holder for the Dust Complex payload for the ExoMars 2022 mission's Surface Science Platform was designed and fabricated in PBF-LB/M. ...
Lightweight structures with an internal lattice infill and a closed shell have received a lot of attention in the last 20 years for satellites, due to their improved stiffness, buckling strength, multifunctional design, and energy absorption. The geometrical freedom typical of Additive Manufacturing allows lighter, stiffer, and more effective structures to be designed for aerospace applications. The Laser Powder Bed Fusion technology, in particular, enables the fabrication of metal parts with complex geometries, altering the way the mechanical components are designed and manufactured. This study proposed a method to re-design the original satellite structures consisting of walls and ribs with an enclosed lattice design. The proposed new structures must comply with restricted requirements in terms of mechanical properties, dimensional accuracy, and weight. The most challenging is the first frequency request which the original satellite design, based on traditional fabrication, does not satisfy. To overcome this problem a particular framework was developed for locally thickening the critical zones of the lattice. The use of the new design permitted complying with the dynamic behavior and to obtain a weight saving maintaining the mechanical properties. The Additive Manufacturing fabrication of this primary structure demonstrated the feasibility of this new technology to satisfy challenging requests in the aerospace field.
... the voxel-based IWP structure representation :a) solid and void phase b) the solid network.The governing equations of 8 TPMS structures surfaces (i.e., IWP, Primitive, Diamond, Diamond-type2, Gyroid, Neovius, FKS, and FRD) investigated as solid networks in this study are given as[43][44][45][46][47][48][49][50]: ...
Triply periodic minimal surfaces (TPMS) are a type of metamaterial that get their unusual properties from the topology of microstructure elements, but they provide non-controllable properties. Utilizing shape memory polymer as a base material, it is possible to control the properties of these structures and create significant and reversible changes in the stiffness, geometry, and performance of metamaterials which could be applicable in many application fields. In this work, the thermal, mechanical, and shape memory behavior of 8 SMP-based TPMS structures has been studied in a wide range of the solid phase volume fractions (i.e., 35–65%). In the thermomechanical analysis, we consider the shape recovery%, the force recovery%, and the shape fixity% as the shape memory properties. For this purpose, the structures were simulated using thermo-visco-hyperelastic constitutive equations. Also, the temperature rate and elastic modulus are considered as the representative thermal and mechanical properties, respectively. Results of this study indicate that the best shape memory and mechanical behaviors belong to the Primitive structure at all different Volume fractions. And the best overall performance for different 8 TPMS structures including the best thermal, mechanical, and thermomechanical behavior accrues at VF = 40% and is sorted as FKS > FRD > Diamond > Diamond-type 2 > Gyroid > IWP > Primitive > Neovious.
... In lightweight structural applications, the octet-truss lattice has great potential due to its stretching-dominated nature. The orientation of the unit cell has a significant influence on the mechanical properties of the lattice structure [1,24]. In previous work, the effect of orientation on the modulus, strength and fracture toughness of octet-truss lattices has been studied using experimental and numerical methods [10,[25][26][27]. ...
... With the help of various analytical models of the lattice materials, the isotropic design of elastic stiffness of lattice materials has been carried out. Xu et al. [22] proposed a concept of controllable anisotropy to combine the two lattice configurations together according to a certain volume fraction so that the relative stiffness along different directions can be controlled. Isotropy in the stiffness can be achieved at a specific combination and volume fraction of lattice configurations. ...
Lattice materials possess excellent mechanical properties such as light weight, high specific stiffness and high energy absorption capacity. However, the commonly used lattice materials inspired by Bravais lattice often give rise to property anisotropy that is not desirable for engineering application such as bone implants. For this sake, a design methodology for isotropic stiffness is proposed in this paper. Firstly, an efficient theoretical method for calculating the elastic matrices of lattice materials was presented. The method is based on Euler–Bernoulli beam theory and the assumption of affine deformation of cell vertices applicable to cubic truss-lattice materials. The theoretical approach was validated by comparing with the finite element simulations. Utilizing the validated theoretical method, and by properly combining the lattice configurations with complementary stiffness along different directions, an elastic isotropic lattice material can be obtained. A few examples are presented to demonstrate the effectiveness and adaptability of the proposed design strategy by permutating the combinations of different classic lattices. The method proposed in this paper can provide a new approach in the design of lattice materials with excellent anisotropy control.
... However, multiple loading conditions are encountered in real-life applications [40][41][42]. One-dimensional FG TPMS structures can perform worse under loading directions other than the parallel direction [43][44][45][46]. There have been limited studies on multidimensional FG TPMS structures to deal with complex loading conditions. ...
Lattice structures based on triply periodic minimum surfaces (TPMS) have received extensive attention due to their superior light-weighting and energy absorption properties. To generate a more competent design to accommodate multi-directional loading conditions in real-life applications, a three-dimensional functionally graded (FG-3D) TPMS structure was proposed in this study. Selective laser melting (SLM) was utilized to fabricate the designed TPMS lattice structures with Ti-6Al-4 V powder. They were investigated experimentally and numerically in terms of mechanical properties under different loading directions. The results indicated that the FG-3D Primitive (P) and Gyroid (G) structures can absorb 45.3% and 12% more energy than the uniform counterparts, respectively, and exhibit excellent energy absorption capacity under different loading directions. In contrast, the mechanical properties of both one- and two-dimensional FG structures might be inferior in some loading directions. Meanwhile, the parametric study of FG-3D structures was conducted and found that a large volume fraction and proper range of gradient variation are preferable for improving the energy absorption capability. These findings can provide guidelines on gradient design strategies, which can promote the application of energy-absorbing structures in real-life engineering.
... This implies that the isotropic lattice structure can be obtained by controlling the w for all volume fractions. Therefore, in addition to the traditional methods for controlling the anisotropy of lattice structures such as adjusting the strut diameter [55,56], designing the hollow struts [57,58], and adjusting the surface morphology [47,59], designing the interpenetrating lattice structures provides a new way to control the structural anisotropy. ...
... Xu et al. [30] studied a method for designing a cellular structure using anisotropic values as a user input. This cellular structure is basically lattice-based. ...
Three-dimensional (3D) printers enable the realization of parts with complex shapes, particularly parts with an internal structure as well as an external shape. They are beginning to be used in real production as well as for prototyping. Because 3D printers allow shapes for parts that could not be imagined when conventional machining processes were the only fabrication methods, designers need to design porous parts with minimum weights that can maintain the required load-bearing capability without concerns about the realization of those parts. However, designers cannot design the internal structure of the parts using the current computer-aided design systems as freely as they can design the external shape. Therefore, in this paper, an intuitive design tool is proposed for users to interactively design an internal structure inside given external shape. To create a porous structure inside given closed volume, we aimed to generate a honeycomb-like structure comprising cells whose size and crowdedness can be intuitively manipulated by a designer. Thus, fine cells exist in certain regions, while coarse cells exist in the remaining regions according to the design. To realize this aim, the phenomenon in which more iron particles are attracted near a magnet and fewer are attracted further away from the magnet is imitated. More and finer honeycomb-like cells are attracted near a magnet located on the external surface of the closed volume. The designer can add magnets and move them on the external surface until the desired internal honeycomb-like structure is obtained.
In order to comprehensively understand the mechanical behavior of biological entities and aerospace applications subjected to hypergravity environments, we delve into the impact of hypergravity on the equivalent compliance of cubic lattice structures. Capitalizing on the periodic spatial distribution, we employ a unit cell methodology to deduce the homogenized stress-strain relationship for the lattice structures, subsequently obtaining the associated equivalent compliance. The equivalent compliance can be conveniently reduced to instances without hypergravity influence. Furthermore, numerical simulations are executed to validate the derivations and to illustrate that hypergravity indeed affects the mechanical properties of lattice structures. We introduce a non-dimensional hypergravity factor, which quantifies the impact of hypergravity magnitude relative to the Young’s modulus of the base material. Our findings reveal that the hypergravity factor influences perpendicular compliance quadratically and parallel compliance linearly. Simultaneously, the perpendicular shear compliance remains unaffected, whereas the parallel shear compliance experiences an inverse effect. Additionally, the lattice structure transforms into a gradient material oriented in the hypergravity direction, consequently generating a scale effect.
With the recent development of additive manufacturing technology represented by 3D printers, various lattice structures have emerged because their mechanical properties can be designed artificially according to their structural characteristics. This study aims to develop knowledge that will contribute to the design of lattice structures with tailored and desired mechanical properties. Among the many unit cell topologies in the lattice structures that have been designed in numerous studies, there are several basic structures and a variety of additional structures that were derived from these basic structures. However, there is a degree of ambiguity as to which of these structures should be regarded as the basic structures. In this study, the basic structures of a lattice structure with orthogonal symmetry were derived by determining the edges of the struts using a mathematical combination approach. Then, the deformation characteristics of them were evaluated through elasto-plastic finite element analysis. Five basic structures were determined by designing the unit cell of the lattice structure such that the struts pass through the vertices, the midpoints of the edges, and the centers of the faces in the cubic design region. It was found that structures with the same strut directions in their unit cells have similar stiffness distributions, and the basic structures obtained can be classified accordingly into three types. Finite element analysis of the compression of a micro-lattice structure composed of these basic structures confirmed that different deformation characteristics appeared during plastic collapse for each type of classified basic structure, and that the strut deformation type determined the overall deformation characteristics. Evaluation of the stiffness and the plastic collapse stress showed that with stretch-dominant strut deformation, lattice structures can be made lighter in weight while still maintaining some stiffness and some plastic collapse stress.
Mechanical Metamaterials (MMs) are artificially designed structures with extraordinary properties that are dependent on micro architectures and spatial tessellations of unit cells, rather than constitutive compositions. They have demonstrated promising and attractive application potentials in practical engineering. Recently, how to rationally design novel MMs and discover their multifunctional behaviors has received tremendous discussions with rapid progress, particularly in the last ten years with an enormous increase of publications and citations. Herein, we present a comprehensive overview of considerable advances of MMs, including critical focuses at different scales, forward and inverse design mechanisms with optimization formulations, micro architectures of unit cells, and their spatial tessellations in discovering novel MMs and future prospects. The implications in clarifying the four focuses at levels from the global to the physical in MMs are highlighted, that is, unique structures designed for unique functions, unique micro unit cells placed in unique locations, unique micro unit cells designed for unique properties and unique micro unit cells evaluated by unique mechanisms. We examine the inverse designs of MMs with intrinsic mechanisms of structure-property driven characteristics to achieve unprecedented behaviors, which are involved into material designs and multiscale designs. The former primarily optimizes micro architectures to explore novel MMs, and the latter focuses on micro architectures and spatial tessellations to promote multifunctional applications of MMs in engineering. Finally, we propose several promising research topics with serious challenges in design formulations, micro architectures, spatial tessellations and industrial applications.
When a cubic lattice packaged by a boundary layer is subjected to a mechanical and temperature load, the force and length change of the bonds are equivalently evaluated by the average stress and strain of the unit cell. Provided a displacement gradient variation at a certain stress state, the variation of stress related to the strain variation provides the effective stiffness of the material at the corresponding configuration. It is discovered that the effective elasticity and thermal expansion coefficient can be tailored by the prestress through the boundary layer, which generates a configurational stress. Because the bonds of a cubic lattice depend on the material types, we consider the harmonic potential of springs for cellular lattices and Hertz's contact potential of balls for granular lattices, respectively. The cubic symmetry of effective elasticity is demonstrated for the three types of cubic lattices. By taking the orientational average, isotropic elastic constants can be obtained for randomly oriented lattices. As the bond length changes with the prestress of the boundary layer and controls the thermoelastic behavior, a novel design method of lattice-based materials confined in a spherical shell is demonstrated to achieve zero thermal expansion and a positive temperature derivative of elasticity.
Low-density, high-strength, ductile metal mechanical metamaterials are in high demand for engineering applications but remain out of reach by the Gibson-Ashby model. Here we demonstrate a new design concept based on a generalized theoretical model or an extended Gibson-Ashby model to overcome this challenge. We show that the deformation mechanism of a strut-based metal lattice material depends on its strut length-to-diameter (l/d) ratio, and the key to maximizing its strength is to reduce its l/d ratio to the minimum manufacturable level without increasing the lattice density. Inspired by this design concept, we investigate three strut remodeling strategies to strengthen metal lattices. Our low-density (1.6 g/cm3) Ti-6Al-4V lattices designed according to Wolff's law of bone remodeling achieve exceptional strength (>400 MPa) compared to all cellular metallic materials of equivalent density reported so far (2-8 times their strength). Our l/d-centered design concept is expected to inspire the design of more metal metamaterials.
The stiffness and toughness of topology optimised structures containing lattices under three-point bending is studied. A porosity constraint is introduced to control the proportion of lattice generated while optimising the beams for minimum compliance. A novel tetrahedron element-based lattice with tapered trusses and a near-isotropic elastic response is developed to accurately map the relative densities from topology optimisation to a 3D printable structure. Topology optimised solid structures (0 % porosity), used for benchmarking, are found to have high stiffness but can be susceptible to buckling. At the other extreme, structures comprising entirely of lattice (100 % porosity) are shown to have low initial stiffness and low residual toughness. An experimental parametric study reveals that porosity can be tailored between these two bounds to achieve both high stiffness and high residual toughness.
The rise of machine learning has fueled the discovery of new materials and, especially, metamaterials -- truss lattices being their most prominent class. While their tailorable properties have been explored extensively, the design of truss-based metamaterials has remained highly limited and often heuristic, due to the vast, discrete design space and the lack of a comprehensive parameterization. We here present a graph-based deep learning generative framework, which combines a variational autoencoder and a property predictor, to construct a reduced, continuous latent representation covering an enormous range of trusses. This unified latent space allows for the fast generation of new designs through simple operations (e.g., traversing the latent space or interpolating between structures). We further demonstrate an optimization framework for the inverse design of trusses with customized properties, including exceptionally stiff, auxetic, and pentamode-like designs. This generative model can predict manufacturable (and counter-intuitive) designs with extreme target properties beyond the training domain.
Developing a functional gradient scaffold compatible with the fantastic biological and mechanical properties of natural bone tissue is imperative in bone tissue engineering. In this work, the stretch-dominated (cubical and circular) and bending-dominant (diamond and gyroid) pore styles were employed to design custom-graded scaffolds based on the curve interference method and then were fabricated by selective laser sintering (SLS) using polyamide 12 (PA12) powder. Subsequently, the mechanical behavior, failure mechanism, and energy absorption performance of porous structures were investigated via compression experiments and finite element (FE) simulation. The results indicated that the stretch-dominated radial gradient structures entire exhibited transverse shear failure and the bending-dominant radial gradient structures whole exhibited progressive destruction, while all of the axial gradient scaffolds suffered a predictable layer-by-layer fracture. Among them, the bending-dominated radial gradient structure of gyroid had been proven to sustain stronger deformability and energy absorption capacity. Meanwhile, the FE method powerfully predicted the mechanical behavior of the scaffold, and this research thereby possessed significant implications for the development of bone tissue engineering.
Lattice structures are known to have high performance-to-weight ratios because of their highly efficient material distribution in a given volume. However, their inherently large void fraction leads to low mechanical properties compared to the base material, high anisotropy, and brittleness. Most works to date have focused on modifying the spatial arrangement of beam elements to overcome these limitations, but only simple beam geometries are adopted due to the infinitely large design space associated with probing and varying beam shapes. Herein, we present an approach to enhance the elastic modulus, strength, and toughness of lattice structures with minimal tradeoffs by optimizing the shape of beam elements for a suite of lattice structures. A generative deep learning-based approach is employed, which leverages the fast inference of neural networks to accelerate the optimization process. Our optimized lattice structures possess superior stiffness (+59%), strength (+49%), toughness (+106%), and isotropy (+645%) compared to benchmark lattices consisting of cylindrical beams. We fabricate our lattice designs using additive manufacturing to validate the optimization approach; experimental and simulation results show good agreement. Remarkable improvement in mechanical properties is shown to be the effect of distributed stress fields and deformation modes subject to beam shape and lattice type.
The 3D auxetic structure (3D-AS) is designed, whose transverse isotropy at small deformations depends strongly on certain geometric parameters. Poisson's ratio and Young's modulus of the 3D-AS in each loading direction are calculated by using the energy method based on the periodic boundary condition at small deformations, and parametric analysis is performed. The effects of θ, t, and b on Poisson's ratio and Young's modulus of the 3D-AS are determined by theoretical analysis, experiments, and numerical simulations. The results show that θ and t are important factors affecting the Poisson's ratio and Young's modulus of 3D-AS, and that b mainly affects Young's modulus. In particular, the transverse isotropy of 3D-AS is analyzed in detail. Through numerical simulations, it is proved that the 3D-AS exhibits transverse isotropic elasticity within a certain parameter range. The 3D-AS exhibits transverse isotropic elasticity in the XY plane when θ ≥ 55°, t ≤ 0.7 mm, or b ≥ 3 mm. The transverse isotropic effective elastic properties can be largely adjusted by modifying the structural geometry. The more desired transverse isotropic elastic properties can be obtained by changing the parameters θ, t, or b of the unit cell. The experimental results agree well with the theoretical analysis and numerical simulations, and prove their accuracy.
Homogenization‐based topology optimization (HMTO) is one of the most extensively used grading methods to generate functionally graded lattice structures (FGLs). However, it requires a pre‐characterization of the lattices, which is time‐consuming. As a remedy, Free‐size Optimization‐based Graded Lattice Generation (FOGLG) is explored as an alternative method to generate the FGLs. This paper builds on the authors’ previous work in which the HMTO and FOGLG approaches are studied to improve the dynamic characteristic of a design by using a single lattice type, namely double gyroid (DG) structure. To show applicability of the proposed methods, different lattice types including Diamond (D), Gyroid (G), and I‐WP are employed to create FGLs in this paper. The frequency response analysis is performed, and the results from HMTO and FOGLG are compared in terms of their accuracy and efficiency. The optimized designs are then reconstructed by relative density mapping (RDM) and enhanced relative density mapping (ERDM) methods. The fabricated test samples made of Cobalt‐Chromium using the Direct Metal Laser Melting (DMLM) technique are then experimentally validated using a laser vibrometer. The results reveal that HMTO and FOGLG can be used on the lattice types with a variety of configurations and relative densities. This article is protected by copyright. All rights reserved.
Pattern transformation in a periodic porous structure has inspired multifarious mechanical metamaterials/metastructures due to the induced unusual negative Poisson's ratio behavior of macroscopic materials. Recently, it has been leveraged to architect a variety of designable and multifunctional structural members. Inspired by this design methodology, a novel porous cylindrical shell, which is perforated by a large number of staggered openings, is constructed and investigated meticulously. A stable, anti‐disturbed, and controllable waisted deformation of the architected cylindrical shell will be triggered under an axial compression. A stoma‐shaped biomimetic hole and graded distribution of initial openings are proposed to ensure that the holes distributed throughout the shell can be closed up concurrently while the closed states of holes can be flexibly programmed. To explore the applications of such shells, a handy cylindrical vessel is elaborately designed and its multiple functions including reagent release, underwater sampling, and flow control are exhibited by experiments. The results reflected that the designed vessel can be facilitated with many advantages such as uniform release, quick action, easy actuation, and repeated usage. Moreover, it also might open a new avenue for metamaterials in the fields of biomedical engineering, underwater detection, fluid machinery, etc. A novel porous cylindrical shell is constructed based on pattern transformation. A stoma‐shaped biomimetic hole and graded distribution of openings are proposed to program the closing states of holes. A cylindrical vessel with arbitrary closing state is established by programming the distribution of holes. Multi‐functional cylindrical vessel can be applied for reagent release, underwater sampling, and flow control.
Architected materials are increasingly applied in form of lattice structures to biomedical implant design for the purpose of optimizing the implant’s biomechanical properties. Since the porous design of the lattice structures affects the resulting properties of the implant, its parameters are being investigated by numerous research articles. The design-related parameters of the unit cells for a strut-architected material are mainly the pore size and the strut thickness. Until today, researchers have not been able to decide on the perfect values of the unit cell parameters for the osseointegration process and tissue regeneration. Based on in vivo and in vitro experiments conducted in the field, researchers have suggested a range of values for the parameters of the lattice structures where osseointegration is in acceptable status. The present study presents a comprehensive review of the research carried out until today, experimenting and proposing the optimum unit cell parameters to generate the most suitable lattice structure for the osseointegration procedure presented in orthopedic applications. Additional recommendations, research gaps, and instructions to improve the selection process of the unit cell parameters are also discussed.
To tackle the challenge in artificial spinal disc (ASD) design of restoring the mechanics of a natural disc, this study proposes an innovative lattice-based ASD for reproducing a patient-specific anisotropic rotational response, inspired by the design freedom provided by lattice structures. Motivated by the great potential of machine learning to improve computational design processes, a method is proposed for computationally efficient topology optimization using artificial neural networks (ANNs) and a subsequent member sizing for automating the design of patient-specific ASDs. The results reported in this study show a good match between the optimized ASDs’ six rotational stiffnesses with those of both L2-L3 and L4-L5 human lumbar discs. Additionally, the fast convergence rate of the optimization verifies the application of ANNs and the proposed strategy to reduce the design space by formulating the design problem as optimizing the unit-cell distribution in a predefined grid. Therefore, the study demonstrates that a lattice-based ASD is able to reproduce patient-specific anisotropic rotational response and that a machine-learning-based method improves the computational efficiency of an automated design process to produce personalized ASD designs.
Aiming at the problem of 3D printing cannot manufacture lattice structure with overhanging rods or nodes, 3D shape approximation and infill algorithms with self-supporting lattice structure are proposed. Firstly, rhombic hexahedron is used as the unit cell and the function of the geometry of the unit cell and its self-supporting property is constructed, a self-supporting unit cell with minimal volume is further generated
which covers the whole input 3D shape. Then the 3D shape is approximated by the iterative subdivision of the unit cells under the constraint of the shortest edge length and the number of subdivisions. Finally, to guarantee the printability of the generated lattice structure, self-supporting struts are added to support the overhanging nodes. In addition, the 3D self-supporting infill structure is generated by the subdivision of unit cells. Experimental models are selected from 3D ShapeNet, and then the algorithms are implemented and the results on VS2010 and MATLAB R2017a are visualized. The results demonstrate the effectiveness and robustness of the proposed algorithms for 3D shape approximation and infill
Ceramics have some of the highest strength- and stiffness-to-weight ratios of any material but are suboptimal for use as structural
materials because of their brittleness and sensitivity to flaws. We demonstrate the creation of structural metamaterials composed
of nanoscale ceramics that are simultaneously ultralight, strong, and energy-absorbing and can recover their original shape
after compressions in excess of 50% strain. Hollow-tube alumina nanolattices were fabricated using two-photon lithography,
atomic layer deposition, and oxygen plasma etching. Structures were made with wall thicknesses of 5 to 60 nanometers and densities
of 6.3 to 258 kilograms per cubic meter. Compression experiments revealed that optimizing the wall thickness-to-radius ratio
of the tubes can suppress brittle fracture in the constituent solid in favor of elastic shell buckling, resulting in ductile-like
deformation and recoverability.
Additive manufacturing, otherwise known as three-dimensional (3D) printing, is driving major innovations in many areas, such as engineering, manufacturing, art, education and medicine. Recent advances have enabled 3D printing of biocompatible materials, cells and supporting components into complex 3D functional living tissues. 3D bioprinting is being applied to regenerative medicine to address the need for tissues and organs suitable for transplantation. Compared with non-biological printing, 3D bioprinting involves additional complexities, such as the choice of materials, cell types, growth and differentiation factors, and technical challenges related to the sensitivities of living cells and the construction of tissues. Addressing these complexities requires the integration of technologies from the fields of engineering, biomaterials science, cell biology, physics and medicine. 3D bioprinting has already been used for the generation and transplantation of several tissues, including multilayered skin, bone, vascular grafts, tracheal splints, heart tissue and cartilaginous structures. Other applications include developing high-throughput 3D-bioprinted tissue models for research, drug discovery and toxicology.
T cells that accompany allogeneic hematopoietic grafts for treating leukemia enhance engraftment and mediate the graft-versus-leukemia
effect. Unfortunately, alloreactive T cells also cause graft-versus-host disease (GVHD). T cell depletion prevents GVHD but
increases the risk of graft rejection and leukemic relapse. In human transplants, we show that donor-versus-recipient natural
killer (NK)–cell alloreactivity could eliminate leukemia relapse and graft rejection and protect patients against GVHD. In
mice, the pretransplant infusion of alloreactive NK cells obviated the need for high-intensity conditioning and reduced GVHD.
NK cell alloreactivity may thus provide a powerful tool for enhancing the efficacy and safety of allogeneic hematopoietic
transplantation.
Additive manufacturing (AM) technology has been researched and developed for more than 20 years. Rather than removing materials, AM processes make three-dimensional parts directly from CAD models by adding materials layer by layer, offering the beneficial ability to build parts with geometric and material complexities that could not be produced by subtractive manufacturing processes. Through intensive research over the past two decades, significant progress has been made in the development and commercialization of new and innovative AM processes, as well as numerous practical applications in aerospace, automotive, biomedical, energy and other fields. This paper reviews the main processes, materials and applications of the current AM technology and presents future research needs for this technology.
Tissue engineering scaffold is a biological substitute that aims to restore, to maintain, or to improve tissue functions. Currently available manufacturing technology, that is, additive manufacturing is essentially applied to fabricate the scaffold according to the predefined computer aided design (CAD) model. To develop scaffold CAD libraries, the polyhedrons could be used in the scaffold libraries development. In this present study, one hundred and nineteen polyhedron models were evaluated according to the established criteria. The proposed criteria included considerations on geometry, manufacturing feasibility, and mechanical strength of these polyhedrons. CAD and finite element (FE) method were employed as tools in evaluation. The result of evaluation revealed that the close-cellular scaffold included truncated octahedron, rhombicuboctahedron, and rhombitruncated
cuboctahedron. In addition, the suitable polyhedrons for using as open-cellular scaffold libraries included hexahedron, truncated octahedron, truncated hexahedron,
cuboctahedron, rhombicuboctahedron, and rhombitruncated cuboctahedron. However, not all pore size to beam thickness ratios (PO : BT) were good for making the open-cellular scaffold. The PO : BT ratio of each library, generating the enclosed pore inside the scaffold, was excluded to avoid the impossibility of material removal after the fabrication. The close-cellular libraries presented the constant porosity
which is irrespective to the different pore sizes. The relationship between PO : BT ratio and porosity of open-cellular scaffold libraries was displayed in the form of Logistic Power function. The possibility of merging two different types of libraries to produce the composite structure was geometrically evaluated in terms of the intersection index and
was mechanically evaluated by means of FE analysis to observe the stress level. The couples of polyhedrons presenting low intersection index and high stress level were excluded. Good couples for producing the reinforced scaffold were
hexahedron-truncated hexahedron and cuboctahedron-rhombitruncated cuboctahedron.
Ultralight (<10 milligrams per cubic centimeter) cellular materials are desirable for thermal insulation; battery electrodes; catalyst supports; and acoustic, vibration, or shock energy damping. We present ultralight materials based on periodic hollow-tube microlattices. These materials are fabricated by starting with a template formed by self-propagating photopolymer waveguide prototyping, coating the template by electroless nickel plating, and subsequently etching away the template. The resulting metallic microlattices exhibit densities ρ ≥ 0.9 milligram per cubic centimeter, complete recovery after compression exceeding 50% strain, and energy absorption similar to elastomers. Young's modulus E scales with density as E ~ ρ(2), in contrast to the E ~ ρ(3) scaling observed for ultralight aerogels and carbon nanotube foams with stochastic architecture. We attribute these properties to structural hierarchy at the nanometer, micrometer, and millimeter scales.
In this paper, we examine prospects for the manufacture of patient-specific biomedical implants replacing hard tissues (bone), particularly knee and hip stems and large bone (femoral) intramedullary rods, using additive manufacturing (AM) by electron beam melting (EBM). Of particular interest is the fabrication of complex functional (biocompatible) mesh arrays. Mesh elements or unit cells can be divided into different regions in order to use different cell designs in different areas of the component to produce various or continually varying (functionally graded) mesh densities. Numerous design elements have been used to fabricate prototypes by AM using EBM of Ti-6Al-4V powders, where the densities have been compared with the elastic (Young) moduli determined by resonant frequency and damping analysis. Density optimization at the bone-implant interface can allow for bone ingrowth and cementless implant components. Computerized tomography (CT) scans of metal (aluminium alloy) foam have also allowed for the building of Ti-6Al-4V foams by embedding the digital-layered scans in computer-aided design or software models for EBM. Variations in mesh complexity and especially strut (or truss) dimensions alter the cooling and solidification rate, which alters the alpha-phase (hexagonal close-packed) microstructure by creating mixtures of alpha/alpha' (martensite) observed by optical and electron metallography. Microindentation hardness measurements are characteristic of these microstructures and microstructure mixtures (alpha/alpha') and sizes.
Periodic cellular metals with honeycomb and corrugated topologies are widely used for the cores of light weight sandwich panel structures. Honeycombs have closed cell pores and are well suited for thermal protection while also providing efficient load support. Corrugated core structures provide less efficient and highly anisotropic load support, but enable cross flow heat exchange opportunities because their pores are continuous in one direction. Recent advances in topology design and fabrication have led to the emergence of lattice truss structures with open cell structures. These three classes of periodic cellular metals can now be fabricated from a wide variety of structural alloys. Many topologies are found to provide adequate stiffness and strength for structural load support when configured as the cores of sandwich panels. Sandwich panels with core relative densities of 2-10% and cell sizes in the millimetre range are being assessed for use as multifunctional structures. The open, three-dimensional interconnected pore networks of lattice truss topologies provide opportunities for simultaneously supporting high stresses while also enabling cross flow heat exchange. These highly compressible structures also provide opportunities for the mitigation of high intensity dynamic loads created by impacts and shock waves in air or water. By filling the voids with polymers and hard ceramics, these structures have also been found to offer significant resistance to penetration by projectiles.
The rigidity of a network of elastic beams crucially depends on the specific
details of its structure. We show both numerically and theoretically that there
is a class of isotropic networks which are stiffer than any other isotropic
network with same density. The elastic moduli of these \textit{stiffest elastic
networks} are explicitly given. They constitute upper-bounds which compete or
improve the well-known Hashin-Shtrikman bounds. We provide a convenient set of
criteria (necessary and sufficient conditions) to identify these networks, and
show that their displacement field under uniform loading conditions is affine
down to the microscopic scale. Finally, examples of such networks with periodic
arrangement are presented, in both two and three dimensions.
This first comprehensive overview of the modern aspects of biomineralization represents life and materials science at its best: Bioinspired pathways are the hot topics in many disciplines and this holds especially true for biomineralization. Here, the editors -- all well-known members of associations and prestigious institutes -- have assembled an international team of renowned authors to provide first-hand research results. From the contents: VOLUME 1: BIOLOGICAL ASPECTS AND STRUCTURE FORMATION. Silica-Hydrated Polysilicondioxide. Iron Sulfides and Oxides. Calcium Carbonates and Sulfates. Calcium Phosphates. VOLUME 2: BIOMIMETIC AND BIOINSPIRED CHEMISTRY. Biometic Model Systems in Biomineralization. The Biomineral Approach to Bionics. Bio-inspired Materials Synthesis. Bio-supported Materials Chemistry. Protein Cages as Size-contrained Reaction Vessels. Encapsulation. Imaging of Internal Nanostructures of Biominerals. VOLUME 3: MEDICAL AND CLINICAL ASPECTS. Bone. Teeth. Pathological Calcifications. An interdisciplinary must-have account, for biochemists, bioinorganic chemists, lecturers in chemistry and biochemistry, materials scientists, biologists, and solid state physicists. With forewords by Jeremy D. Pickett-Heaps, Stephen Mann, and Wolfgang Pompe.
Most AM processes require post-processing after part building to prepare the part for its intended form, fit and/or function. Depending upon the AM technique, the reason for post-processing varies. For purposes of simplicity, this chapter will focus on post-processing techniques which are used to enhance components or overcome AM limitations. These include:
Preface to the first edition Preface to the second edition 1. Materials: structure, properties and performance 2. Elasticity and viscoelasticity 3. Plasticity 4. Imperfections: point and line defects 5. Imperfections: interfacial and volumetric defects 6. Geometry of deformation and work-hardening 7. Fracture: macroscopic aspects 8. Fracture: microscopic aspects 9. Fracture testing 10. Solid solution, precipitation and dispersion strengthening 11. Martensitic transformation 12. Speciality materials: intermetallics and foams 13. Creep and superplasticity 14. Fatigue 15. Composite materials 16. Environmental effects.
Cellular solids include engineering honeycombs and foams (which can now be made from polymers, metals, ceramics, and composites) as well as natural materials, such as wood, cork, and cancellous bone. This new edition of a classic work details current understanding of the structure and mechanical behavior of cellular materials, and the ways in which they can be exploited in engineering design. Gibson and Ashby have brought the book completely up to date, including new work on processing of metallic and ceramic foams and on the mechanical, electrical and acoustic properties of cellular solids. Data for commercially available foams are presented on material property charts; two new case studies show how the charts are used for selection of foams in engineering design. Over 150 references appearing in the literature since the publication of the first edition are cited. It will be of interest to graduate students and researchers in materials science and engineering.
There has been considerable interest in materials exhibiting negative or zero compressibility. Such
materials are desirable for various applications. A number of models or mechanisms have been proposed
to characterize the unusual phenomena of negative linear compressibility (NLC) and negative area
compressibility (NAC) in natural or synthetic systems. In this paper we propose a general design technique
for finding metamaterials with negative or zero compressibility by using a topology optimization
approach. Based on the bi-directional evolutionary structural optimization (BESO) method, we establish a
systematic computational procedure and present a series of designs of orthotropic materials with various
magnitudes of negative compressibility, or with zero compressibility, in one or two directions. A physical
prototype of one of such metamaterials is fabricated using a 3D printer and tested in the laboratory under
either unidirectional loading or triaxial compression. The experimental results compare well with the
numerical predictions. This research has demonstrated the feasibility of designing and fabricating
metamaterials with negative or zero compressibility and paved the way towards their practical
applications.
Treatment of large segmental bone defects, especially in load bearing areas, is a complex procedure in orthopedic surgery. The usage of additive manufacturing processes enables the creation of customized bone implants with arbitrary open-porous structure satisfying both the mechanical and the biological requirements for a sufficient bone ingrowth. Aim of the present numerical study was to optimize the geometrical parameters of open-porous titanium scaffolds to match the elastic properties of human cortical bone with respect to an adequate pore size. Three different scaffold designs (cubic, diagonal and pyramidal) were numerically investigated by using an optimization approach. Beam elements were used to create the lattice structures of the scaffolds. The design parameters strut diameter and pore size ranged from 0.2 to 1.5 mm and from 0 to 3.0 mm, respectively. In a first optimization step, the geometrical parameters were varied under uniaxial compression to obtain a structural modulus of 15 GPa (Young׳s modulus of cortical bone) and a pore size of 800 µm was aimed to enable cell ingrowth. Furthermore, the mechanical behavior of the optimized structures under bending and torsion was investigated. Results for bending modulus were between 9.0 and 14.5 GPa. In contrast, shear modulus was lowest for cubic and pyramidal design of approximately 1 GPa. Here, the diagonal design revealed a modulus of nearly 20 GPa. In a second step, large-sized bone scaffolds were created and placed in a biomechanical loading situation within a 30 mm segmental femoral defect, stabilized with an osteosynthesis plate and loaded with physiological muscle forces. Strut diameter for the 17 sections of each scaffold was optimized independently in order to match the biomechanical stability of intact bone. For each design, highest strut diameter was found at the dorsal/medial site of the defect and smallest strut diameter in the center. In conclusion, we demonstrated the possibility of providing optimized open-porous scaffolds for bone regeneration by considering both mechanical and biological aspects. Furthermore, the results revealed the need of the investigation and comparison of different load scenarios (compression, bending and torsion) as well as complex biomechanical loading for a profound characterization of different scaffold designs. The usage of a numerical optimization process was proven to be a feasible tool to reduce the amount of the required titanium material without influencing the biomechanical performance of the scaffold negatively. By using fully parameterized models, the optimization approach is adaptable to other scaffold designs and bone defect situations.
Cellular structures with highly controlled micro-architectures are promising materials for orthopedic applications that require bone-substituting biomaterials or implants. The availability of additive manufacturing techniques has enabled manufacturing of biomaterials made of one or multiple types of unit cells. The diamond lattice unit cell is one of the relatively new types of unit cells that are used in manufacturing of regular porous biomaterials. As opposed to many other types of unit cells, there is currently no analytical solution that could be used for prediction of the mechanical properties of cellular structures made of the diamond lattice unit cells. In this paper, we present new analytical solutions and closed-form relationships for predicting the elastic modulus, Poisson's ratio, critical buckling load, and yield (plateau) stress of cellular structures made of the diamond lattice unit cell. The mechanical properties predicted using the analytical solutions are compared with those obtained using finite element models. A number of solid and porous titanium (Ti6Al4V) specimens were manufactured using selective laser melting. A series of experiments were then performed to determine the mechanical properties of the matrix material and cellular structures. The experimentally measured mechanical properties were compared with those obtained using analytical solutions and finite element (FE) models. It has been shown that, for small apparent density values, the mechanical properties obtained using analytical and numerical solutions are in agreement with each other and with experimental observations. The properties estimated using an analytical solution based on the Euler-Bernoulli theory markedly deviated from experimental results for large apparent density values. The mechanical properties estimated using FE models and another analytical solution based on the Timoshenko beam theory better matched the experimental observations.
Advances introduced by additive manufacturing have significantly improved the ability to tailor scaffolds architecture, enhancing the control over microstructural features. This has led to a growing interest in the development of innovative scaffold designs, as testified by the increasing amount of research activities devoted to the understanding of the correlation between scaffold topological features and its resulting properties, in order to find architectures capable to optimally trade-off between often conflicting requirements (such as the biological and the mechanical ones). Main aim of this article is to provide a review and propose a classification of existing methodologies for scaffold design and optimization in order to address key issues and help in deciphering the complex link between design criteria and resulting scaffold properties.
An orthotropic material is characterized by nine independent moduli. The ratios between the Young’s moduli in three directions are indicative of the level of orthotropy and the bulk modulus is indicative of the overall stiffness. In this paper we propose a method for designing the stiffest orthotropic material which has prescribed ratios for Young’s moduli. The material is modeled as a microstructure in a periodic unit cell. By using the homogenization method, the elasticity tensors are calculated and its compliance matrix is derived. A Lagrangian function is constructed to combine the objective and multiple equality constraints. To enable a bi-section search algorithm, the upper and lower bounds on those multipliers are derived by using a strain energy approach. The overall optimization is based on the bi-directional evolutionary structural optimization (BESO) method. Examples of various orthotropy ratios are investigated. The topology presents a constant pattern of material re-distributed along the strongest axis while the overall stiffness is maintained.
Cellular solids include engineering honeycombs and foams (which can now be made from polymers, metals, ceramics, and composites) as well as natural materials, such as wood, cork, and cancellous bone. This new edition of a classic work details current understanding of the structure and mechanical behavior of cellular materials, and the ways in which they can be exploited in engineering design. Gibson and Ashby have brought the book completely up to date, including new work on processing of metallic and ceramic foams and on the mechanical, electrical and acoustic properties of cellular solids. Data for commercially available foams are presented on material property charts; two new case studies show how the charts are used for selection of foams in engineering design. Over 150 references appearing in the literature since the publication of the first edition are cited. It will be of interest to graduate students and researchers in materials science and engineering. © Lorna J. Gibson and Michael F. Ashby, 1988 and Lorna J. Gibson and Michael F. Ashby, 1997.
This paper demonstrates a simple finite element implementation of Lagrange multipliers to model the mechanical behaviour of an orthotropic composite material. The research shows the proper set of kinematic boundary conditions that must be applied in 2D plane stress elasticity to achieve the correct unit strain vectors that, upon interrogation of the associated Lagrange multipliers, give the stresses induced by these strain vectors. From these stresses the terms in the elasticity matrix can be evaluated. As well as demonstrating the correct kinematic conditions required, the paper presents the consequences of applying intuitive but incorrect conditions. © 1997 John Wiley & Sons, Ltd.
Rapid prototyping allows titanium porous parts with mechanical properties close to that of bone tissue to be obtained. In this article, porous parts of the Ti-6Al-4V alloy with three levels of porosity were obtained by selective laser melting with two different energy inputs. Thermal treatments were performed to determine the influence of the microstructure on the mechanical properties. The porous parts were characterized by both optical and scanning electron microscopy. The effective modulus, yield and ultimate compressive strength were determined by compressive tests. The martensitic α' microstructure was observed in all of the as-processed parts. The struts resulting from the processing conditions investigated were thinner than those defined by CAD models, and consequently, larger pores and a higher experimental porosity were achieved. The use of the high-energy input parameters produced parts with higher oxygen and nitrogen content, their struts that were even thinner and contained a homogeneous porosity distribution. Greater mechanical properties for a given relative density were obtained using the high-energy input parameters. The as-quenched martensitic parts showed yield and ultimate compressive strengths similar to the as-processed parts, and these were greater than those observed for the fully annealed samples that had the lamellar microstructure of the equilibrium α+β phases. The effective modulus was not significantly influenced by the thermal treatments. A comparison between these results and those of porous parts with similar geometry obtained by selective electron beam melting shows that the use of a laser allows parts with higher mechanical properties for a given relative density to be obtained.
Resonant ultrasound spectroscopy (RUS) allows to accurately characterize the complete set of elastic constants of an anisotropic material from a set of measured mechanical resonant frequencies of a specimen. This method does not suffer from the drawbacks and limitations of the conventional sound velocity approach, but has been reported to fail to measure bone because of its strong viscoelastic damping. In this study, we take advantage of recent developments of RUS to overcome this limitation. The frequency response of a human cortical bone specimen (about 5×7×7mm(3)) was measured between 100 and 280kHz. Despite an important overlapping of the resonant peaks 20 resonant frequencies could be retrieved by using a dedicated signal processing method. The experimental frequencies were progressively matched to the frequencies predicted by a model of the sample whose elastic constants were adjusted. The determined diagonal elastic constants were in good agreement with concurrent sound velocity measurements performed in the principal directions of the specimen. This study demonstrates that RUS is suitable for an accurate measurement of cortical bone anisotropic elasticity. In particular, precision of measured Young and shear moduli is about 0.5%.
The linking of computational design with precision solid freeform fabrication has tremendous potential for producing tissue scaffolds with tailored properties. We consider a new approach to optimizing the architecture of scaffolds based on jointly maximizing scaffold stiffness and diffusive transport in the interconnected pores. The stiffness of the scaffolds is matched to that of bone by choosing a suitable scaffold porosity. Moreover, the templates can be scaled to achieve target pore sizes whilst preserving their elastic and diffusive properties. The resultant structures have two major design benefits. First, the scaffolds do not have directions of low stiffness. In contrast, the Young's modulus of conventional layered-grid designs can be 86% less under diagonally-aligned loads than under axis-aligned loads. Second, the mass of the scaffold is used efficiently throughout the structure rather than being clumped in non load-bearing regions. We fabricate prototypes of the implants using selective laser melting and test their elastic properties. Excellent agreement between theory and experiment provides important confirmation of the viability of this route to scaffold design and fabrication.
In this paper, a 3D macro/micro finite element analysis (FEA) modeling approach and a 3D macro/micro analytical modeling approach are proposed for predicting the failure strengths of 3D orthogonal woven CFRP composites. These approaches include two different scale levels, macro- and micro-level. At the macro-level, a relatively coarse structural model is used to study the overall response of the structure. At the micro-level, the laminate block microstructure is modeled in detail for investigating the failure mechanisms of 3D orthogonal woven CFRP composites. The FEA and analytical models developed previously [Tan P, Tong L, Steven GP. Modeling approaches for 3D orthogonal woven composites, Journal of Reinforced Plastics and Composites, 1998:17;545–577] are employed to predict the mechanical properties of 3D orthogonal woven CFRP composites. All models presented in this paper are validated by comparing the relevant predictions with the experimental results, which were reported earlier in Part I of the paper [Tan P, Tong L, Steven GP. Behavior of 3D orthogonal woven CFRP composites. Part I. Experimental investigation, Composites, Part A: Applied Science and Manufacturing, 2000:31;259–71]. The comparison shows that there is a good agreement for the mechanical properties. An acceptable agreement exists for the failure strength in the x or stuffer yarn direction even though the FEA model gives a lower bound and the analytical model gives an upper bound. However, for the failure strength in the y or filler yarn direction, the difference between the predicted and experimental results is significant due to primarily ignoring of the waviness of filler yarn in the models. A curved beam model, which considers the waviness of the filler yarn, will be presented in Part III of the paper.
This paper presents a simple method for structural optimization with frequency constraints. The structure is modelled by a fine mesh of finite elements. At the end of each eigenvalue analysis, part of the material is removed from the structure so that the frequencies of the resulting structure will be shifted towards a desired direction. A sensitivity number indicating the optimum locations for such material elimination is derived. This sensitivity number can be easily calculated for each element using the information of the eigenvalue solution. The significance of such an evolutionary structural optimization (ESO) method lies in its simplicity in achieving shape and topology optimization for both static and dynamic problems. In this paper, the ESO method is applied to a wide range of frequency optimization problems, which include maximizing or minimizing a chosen frequency of a structure, keeping a chosen frequency constant, maximizing the gap of arbitrarily given two frequencies, as well as considerations of multiple frequency constraints. The proposed ESO method is verified through several examples whose solutions may be obtained by other methods.
Selective electron beam melting (SEBM) was successfully used to fabricate novel cellular Ti–6Al–4V structures for orthopaedic applications. Micro computer tomography (μCT) analysis demonstrated the capability to fabricate three-dimensional structures with an interconnected porosity and pore sizes suitable for tissue ingrowth and vascularization. Mechanical properties, such as compressive strength and elastic modulus, of the tested structures were similar to those of human bone. Thus, stress-shielding effects after implantation might be avoided due to a reduced stiffness mismatch between implant and bone. A chemical surface modification using HCl and NaOH induced apatite formation during in vitro bioactivity tests in simulated body fluid under dynamic conditions. The modified bioactive surface is expected to enhance the fixation of the implant in the surrounding bone as well as to improve its long-term stability.
We present a basic analysis that establishes the metrics affecting the energy absorbed by multilayer cellular media during irreversible compaction on either a mass or volume basis. The behaviors at low and high impulse levels are distinguished through the energy dissipated in the shock. The overall mass of an energy absorbing system (comprising a cellular medium and a buffer) is minimized by maximizing the non-dimensional dissipation per unit mass parameter for the cellular medium, Λ≡Umρs/σY, where Um is the dissipation per unit mass of the cellular medium, ascertained from the area under the quasi-static compressive stress/strain curve, σY the yield strength of the constituent material and ρs the density of the material used in the medium. Plots of Λ against the non-dimensional stress transmitted through the medium, σtr/σY demonstrate the relative energy absorbing characteristics of foams and prismatic media, such as honeycombs. Comparisons with these benchmark systems are used to demonstrate the superior performance of micro-lattices, especially those with hollow truss members. Numerical calculations demonstrate the relative densities and geometric configurations wherein the lattices offer benefit. Experimental results obtained for a Ni micro-lattice with hollow members not only affirm the benefits, but also demonstrate energy absorption levels substantially exceeding those predicted by analysis. This assessment highlights the new opportunities that tailored micro-lattices provide for unprecedented levels of energy absorption for protection from impulsive loads.
Popularization of portable electronics and electric vehicles worldwide stimulates the development of energy storage devices, such as batteries and supercapacitors, toward higher power density and energy density, which significantly depends upon the advancement of new materials used in these devices. Moreover, energy storage materials play a key role in efficient, clean, and versatile use of energy, and are crucial for the exploitation of renewable energy. Therefore, energy storage materials cover a wide range of materials and have been receiving intensive attention from research and development to industrialization. In this Review, firstly a general introduction is given to several typical energy storage systems, including thermal, mechanical, electromagnetic, hydrogen, and electrochemical energy storage. Then the current status of high-performance hydrogen storage materials for on-board applications and electrochemical energy storage materials for lithium-ion batteries and supercapacitors is introduced in detail. The strategies for developing these advanced energy storage materials, including nanostructuring, nano-/microcombination, hybridization, pore-structure control, configuration design, surface modification, and composition optimization, are discussed. Finally, the future trends and prospects in the development of advanced energy storage materials are highlighted.
Patient specific porous implants for the reconstruction of craniofacial defects have gained importance due to their better performance over their generic counterparts. The recent introduction of electron beam melting (EBM) for the processing of titanium has led to a one step fabrication of porous custom titanium implants with controlled porosity to meet the requirements of the anatomy and functions at the region of implantation. This paper discusses an image based micro-structural analysis and the mechanical characterization of porous Ti6Al4V structures fabricated using the EBM rapid manufacturing process. SEM studies have indicated the complete melting of the powder material with no evidence of poor inter-layer bonding. Micro-CT scan analysis of the samples indicate well formed titanium struts and fully interconnected pores with porosities varying from 49.75%-70.32%. Compression tests of the samples showed effective stiffness values ranging from 0.57(+/-0.05)-2.92(+/-0.17)GPa and compressive strength values of 7.28(+/-0.93)-163.02(+/-11.98)MPa. For nearly the same porosity values of 49.75% and 50.75%, with a variation in only the strut thickness in the sample sets, the compressive stiffness and strength decreased significantly from 2.92 GPa to 0.57 GPa (80.5% reduction) and 163.02 MPa to 7.28 MPa (93.54 % reduction) respectively. The grain density of the fabricated Ti6Al4V structures was found to be 4.423 g/cm(3) equivalent to that of dense Ti6Al4V parts fabricated using conventional methods. In conclusion, from a mechanical strength viewpoint, we have found that the porous structures produced by the electron beam melting process present a promising rapid manufacturing process for the direct fabrication of customized titanium implants for enabling personalized medicine.
Musculoskeletal tissue, bone and cartilage are under extensive investigation in tissue engineering research. A number of biodegradable and bioresorbable materials, as well as scaffold designs, have been experimentally and/or clinically studied. Ideally, a scaffold should have the following characteristics: (i) three-dimensional and highly porous with an interconnected pore network for cell growth and flow transport of nutrients and metabolic waste; (ii) biocompatible and bioresorbable with a controllable degradation and resorption rate to match cell/tissue growth in vitro and/or in vivo; (iii) suitable surface chemistry for cell attachment, proliferation, and differentiation and (iv) mechanical properties to match those of the tissues at the site of implantation. This paper reviews research on the tissue engineering of bone and cartilage from the polymeric scaffold point of view.
Porosity and pore size of biomaterial scaffolds play a critical role in bone formation in vitro and in vivo. This review explores the state of knowledge regarding the relationship between porosity and pore size of biomaterials used for bone regeneration. The effect of these morphological features on osteogenesis in vitro and in vivo, as well as relationships to mechanical properties of the scaffolds, are addressed. In vitro, lower porosity stimulates osteogenesis by suppressing cell proliferation and forcing cell aggregation. In contrast, in vivo, higher porosity and pore size result in greater bone ingrowth, a conclusion that is supported by the absence of reports that show enhanced osteogenic outcomes for scaffolds with low void volumes. However, this trend results in diminished mechanical properties, thereby setting an upper functional limit for pore size and porosity. Thus, a balance must be reached depending on the repair, rate of remodeling and rate of degradation of the scaffold material. Based on early studies, the minimum requirement for pore size is considered to be approximately 100 microm due to cell size, migration requirements and transport. However, pore sizes >300 microm are recommended, due to enhanced new bone formation and the formation of capillaries. Because of vascularization, pore size has been shown to affect the progression of osteogenesis. Small pores favored hypoxic conditions and induced osteochondral formation before osteogenesis, while large pores, that are well-vascularized, lead to direct osteogenesis (without preceding cartilage formation). Gradients in pore sizes are recommended for future studies focused on the formation of multiple tissues and tissue interfaces. New fabrication techniques, such as solid-free form fabrication, can potentially be used to generate scaffolds with morphological and mechanical properties more selectively designed to meet the specificity of bone-repair needs.
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