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Design of dimpled tubular structures for energy absorption
... The experimentally validated FEM results showed that the collapse of axially crushed circular tubes could be guided by the pre-folded origami patterns, along with significantly enhanced energy absorption capacity. Later, Yang et al. [16] proposed another novel tube with predesigned ellipsoidal dimples on the tube surface. The results showed that with proper parameter designs the initial peak force and the fluctuation in the plateau region could be significantly reduced, without substantially sacrificing the mean crushing force. ...
... The full-diamond tube [15] was composed of Yoshimura-pattern, which had been found in axial crushing tests of circular tubes [17]. The dimpled tube [16] consisted of ellipsoidal dimples with staggered vertical and horizontal patterns concaving outward and inward. The new origami tubes studied in this paper were designed with the same dimensions as the dimpled ones with the height (H) of 100 mm and the diameter (D) of 47.75 mm. ...
... The finite element modelling was validated by uniaxial compression tests on 3D printed brass tubes following the previous work by the authors [16]. The tests were conducted on MTS machine (type 810) with the crushing speed setting at 10 -4 m/s to guarantee the quasi-static condition. ...
In this paper, the crushing performance of two novel types of tubular structures with predesigned Yoshimura-pattern and ellipsoidal dimples were studied by using finite element modelling and compared with conventional circular tubes. The influence of structural arrangement of representative structural units and material properties on the mechanical response of full-diamond tubes was identified. The results showed that properly designed origami tubes had substantially lower initial peak force, higher mean crushing force and remarkably less fluctuation of crushing force than the conventional circular and dimpled tubes. Moreover, the mean crushing force of origami tubes were highly sensitive to material constitutive relations.
... Ren et al. [97] established two tubular structure models by random cut method [98] and vertical-horizontal (V-H) cut method. While previously mentioned auxetic tubular structures are either porous or comprise at least two phases, a nonporous auxetic tubular structure was proposed by Yang et al. [99,100], in which predesigned ellipsoidal dimples were introduced into conventional circular tubes. It's noted that the auxetic behaviour is induced by an ovel mechanism which exploits the out-of-plane deformation of the spherical dimples. ...
... To overcome these shortcomings, many methods have been proposed to improve the design. Yang et al. [100] systematically investigated the influence of different design parameters on the energy absorption of dimpled tubes via numerical simulations and experiments. It is found that properly designed dimpled tubes had substantially lower initial peak force and remarkably less fluctuation in the crushing force than circular tubes, without significantly sacrificing the mean crushing force. ...
Auxetic materials and structures have attracted increasing attention because of their extraordinary mechanical properties. Various types of auxetic tubular structures have been designed and studied in diverse fields, including mechanical and medical engineering. In this paper, design methods and advanced manufacturing technologies of auxetic tubular structures are extensively reviewed, including various types of cellular auxetic tubes, nonporous and porous auxetic tubes, macro and micro auxetic tubes. Furthermore, auxetic behaviour, mechanical properties and potential applications of auxetic tubular structures are elaborated. Finally, the challenges and opportunities on the auxetic tubes are discussed to inspire future research work.
... Using different patterns, Yang et al. [108] proposed a novel type of tubular structure, in which predesigned ellipsoidal dimples were introduced into conventional circular tubes. The proposed tubes were manufactured using a 3D printing technique. ...
... Therefore, Tian et al. [123] comprehensively investigated the crushing behaviour of thin-walled Table 6 Energy absorption characteristics of the folded tubes. [108] tubes with non-uniform groove depth under the oblique loading condition. They indicated that tubes in which the groove depth decreased from the loading end to the fixed end had the best performance, and vice versa. ...
... The final crushed displacement was set as 90 mm, i.e., 90% of the initial height of specimen. The material properties defined in the modelling used the true stress-strain curve obtained from uniaxial tensile tests on brass dog-bone specimens [27], and the mean values of the mechanical properties were: density, ρ = 8671 kg/m 3 ; Young's modulus, E = 49.51 GPa; and yield strength, σ y = 138.62 ...
... where, σ was the mean stress in the strain range 0 ≤ ε ≤ ε u ; and ε u was the ultimate strain for the material, which was calculated by the energy efficiency method [28] based on the engineering stress-strain curves obtained from uniaxial tensile tests on brass dog-bone specimens [27]. ...
Three novel types of multi-cell tubular structures with pre-folded origami patterns were proposed in this paper, aimed at reducing the initial peak force and the crushing force fluctuation while maintaining or increasing the specific energy absorption during uniaxial crush. Experimentally validated finite element modelling was conducted to study the influence of geometric parameters on the mechanical properties. Optimal designs were obtained through multi-objective optimization. The results showed that predesigned origami patterns governed the buckling process of the tubes and quintuple-cell origami tubes could absorb the highest energy in crush with significantly reduced initial peak force and the crushing force fluctuation.
... In recent years, the origami structure has been widely used as a metamaterial in the engineering field [23][24][25][26]. The creases in the origami structure are similar to the "initial geometric defects", which can spread external forces and accelerate the spread of structural deformation to the undeformed area, thereby dissipating energy and improving the mechanical properties of the buffer structure [14,[27][28][29][30][31][32]. Zhang et al. [30] constructed two types of patterns by introducing basic pyramid elements on the surface of thin-walled square tubes. ...
Honeycomb structures have a wide range of applications owing to their light weight and promising energy absorption features. However, a conventional honeycomb structure is designed to absorb impact energy only in the out-of-plane direction and demonstrates unsatisfactory performance when the impact energy originates from a different direction. In this study, we proposed an origami honeycomb structure with the aim of providing an approximately isotropic energy absorption performance. The structure was created by folding a conventional honeycomb structure based on the Miura origami pattern, and it was investigated using both numerical and experimental approaches. Investigations of the structural behaviors under both out-of-plane and in-plane compressions were conducted, and the results revealed significantly different deformation modes in comparison with those of a conventional honeycomb structure. To determine the influences of geometries, we conducted a series of numerical studies, considering various structural parameters, and analyzed the response surface of the mean stress in three directions. Based on the numerical and experimental results, a parameter indicating the approximate isotropy of the origami honeycomb structure was introduced. The proposed structure is promising for absorbing energy from any direction and has potential applications in future metamaterial design work.
... Prior to the maturation of metal additive manufacturing (AM) technologies, honeycombs [1][2][3][4][5], metal foams [6][7][8], and hollow tubes [9][10][11][12][13] were commonly used for energy absorption applications beyond the reach of polymers due to large impact energies and velocities, such as in automotive crumple zones and aerospace crash protection [14,15]. With the additional design freedom enabled by additive manufacturing comes the opportunity to exploit cellular shapes beyond periodic honeycombs and stochastic foams to further optimize energy absorption properties and/or reduce the mass of the structure needed to meet design requirements. ...
A designer of metallic energy absorption structures using additively manufactured cellular materials must address the question of which of a multitude of cell shapes to select from, the majority of which are classified as either honeycomb, beam-lattice, or Triply Periodic Minimal Surface (TPMS) structures. Furthermore, there is more than one criterion that needs to be assessed to make this selection. In this work, six cellular structures (hexagonal honeycomb, auxetic and Voronoi lattice, and diamond, gyroid, and Schwarz-P TPMS) spanning all three types were studied under quasistatic compression and compared to each other in the context of the energy absorption metrics of most relevance to a designer. These shapes were also separately studied with tubes enclosing them. All of the structures were fabricated out of AlSi10Mg with the laser powder bed fusion (PBF-LB. or LPBF) process. Experimental results were assessed in the context of four criteria: the relationship between the specific energy absorption (SEA) and maximum transmitted stress, the undulation of the stress plateau, the densification efficiency, and the design tunability of the shapes tested—the latter two are proposed here for the first time. Failure mechanisms were studied in depth to relate them to the observed mechanical response. The results reveal that auxetic and Voronoi lattice structures have low SEA relative to maximum transmitted stresses, and low densification efficiencies, but are highly tunable. TPMS structures on the other hand, in particular the diamond and gyroid shapes, had the best overall performance, with the honeycomb structures between the two groups. Enclosing cellular structures in tubes increased peak stress while also increasing plateau stress undulations.
... Therefore, composites can potentially provide superior specific energy absorption capabilities over metals [9]. However, whether they are constructed from metals or composites, the axial crushing behavior of straight-walled tubes is usually characterized by a relatively high initial peak force and drastic force reduction in the force-displacement curve [10]. This implies the inefficiency of the straight-walled tubes in their energy absorption performances. ...
Pre-folded tubes can exhibit superior energy absorption characteristics under axial crushing compared to conventional straight-walled tubes. However, their construction can be difficult to automate. In this investigation, we present a novel filament winding approach to efficiently manufacture pre-folded carbon fiber reinforced plastic (CFRP) tubes featuring the Kresling fold pattern. We experimentally study the quasi-static axial crushing behavior of three Kresling geometries and compare them to conventional tubes with a circular and square cross-section. The data from experiments is used to develop a finite element model for estimating axial crush indicators. Despite the layup sequence not orienting the fibers in the direction of loading, we obtain superior structural performance in terms of the mean force divided by the initial peak crushing force, which represents the crushing force efficiency of the structure. The tested tubes exhibit further potential to improve their energy absorption performances, while preserving enhanced manufacturability.
... In the last few years, theoretical prediction [19][20][21], experimental analysis [22][23][24], and numerical study [25][26][27] have been the three main research methods to investigate the crashworthiness of thin-walled structures under different loading conditions. Among them, the expression for the mean crushing force can be derived and modified by theoretical analysis; however, it is difficult to analyze the deformation details of the collapse mode of thin-walled structures through theoretical study. ...
Owing to deformation in the form of the diamond mode with high-energy absorption capacity, origami thin-walled tubes have attracted considerable attention in recent years. Stamping and welding are mainly employed to produce different types of origami thin-walled tubes. The processing defects and geometric asymmetry may be caused by the manufacturing process, which changes the collapsed mode and decreases the energy-absorbing capacity. In this study, fused filament fabrication (FFF) 3D printing is used to fabricate the origami-ending tube (OET) by integrated formation. Experiments and numerical simulations were conducted to study the influence of loading rate and temperature on the energy absorption of polymeric origami tubes under quasi-static loading. The experiments showed that different constitutive models are needed to capture the complex true stress–strain behavior of 3D printing polylactic acid (PLA) material at different temperatures. The damage model is established and then applied to the numerical simulations, which could predict the collapsed mode and the damage behavior of the OET tubes under different loading rates at 30 °C, 40 °C, and 50 °C. Based on the experiments and the validated numerical model, the influence of loading rate and temperature on the crashworthiness performance of the OET tubes is analyzed.
... Auxetic tubular structures exhibit excellent energy absorption properties [51][52][53][54][55] and can be used as energyabsorber. Studies have also shown that stretched tubular structures can be used as fasteners and nails [56,57]. ...
Auxetic materials and structures have received extensive attention due to their unusual behavior. As one of the structures that can realize the auxetic effect, the elliptic perforated structure has been recently developed, but the previous research on the elliptic perforated is limited to the small deformation stage. At the end of the small deformation stage, the elliptic perforated structure becomes dense and loses the auxetic effect. The available compression stroke is very short and therefore the structure has relatively lower specific energy absorption (SEA). In order to make better use of material, through the buckling of lightweight perforated plates, a newly designed re-entrant elliptical perforated structure is proposed in this work. The re-entrant cells rotate and move inward (the first stage), and finally be compressed by neighbor ones (the second stage). Therefore, the structure undergoes rotational deformation in stage one same as previous perforated plates but specific re-entrant deformation in the second stage, thereby realizing the auxeticity in large deformation. Experimental and numerical results show that the stress–strain curve exhibits double platforms, and the novel structure possesses the auxetic effect throughout the whole compression process. Subsequently, a parametric analysis of the re-entrant distance and the ratio of horizontal and vertical wall thickness was carried out for obtaining greater auxetic effect and better stability of the novel re-entrant elliptic perforated structure. The material utilization rate of the re-entrant elliptic perforated plate was greatly improved, and the application prospect of the re-entrant elliptic perforated was also discussed.
... Auxetic tubular structures exhibit multifunctional and unusual performance, such as impact resistance performance [42,43], bending performance [44] and synclastic behaviour [45]. Based on this, widely studies have been implemented on auxetic tubular structures towards exploring their applications as adjustable medical and energy-absorbing devices. ...
Concrete-filled stainless steel tube (CFSST) members take advantage of the high strength and the outstanding corrosion resistance to act as an important role in civil engineering structures. However, the steel tube could not provide the perfect confinement effect for the core concrete during the initial elastic compression stage because Poisson’s ratio of the concrete is smaller than that of the stainless steel tube (SST). In this paper, a novel concrete-filled auxetic stainless steel tube (CFASST) composite structure was designed and manufactured to actively restrain the concrete, making the best use of the desirable deformation characteristics of auxetic tubular structures. The axial compressive performance of these CFASST members and their control factors were investigated experimentally and numerically. Test results were discussed in detail which included failure modes, load versus displacement curves and strain analysis. Finally, parametric analyses were conducted to further study the effects of different parameters (Poisson’s ratio, thickness of the stainless tube) on the CFSST composite structure under axial compression. It was found that CFASST composite structures possess an unusual deformation mode and an improved confinement effect.
... An ideal energy absorber has a long, flat plateau that is just below the peak stress that will damage the object being protected -and it must absorb all the energy needed from it prior to reaching densification. Hollow tubes [140][141][142][143][144], honeycombs [145][146][147][148][149], and metal foams [150][151][152] have been used for these applications since their behaviour approaches that of an ideal energy absorber. Once the force-displacement curve shown in Figure 13a is converted into an effective stress-strain curve, several metrics may be defined to enable comparison across different energy absorber designs and materials. ...
Additive manufacturing (AM) refers to a collection of manufacturing methods involving the incremental addition of material to build a part directly in its final or near-final geometry, usually in a layer-by-layer process. Metal AM in particular has seen great industrial adoption and maturation. This technology enables increased freedom of design in engineered materials with complex geometries, of which architected cellular or lattice structures are particularly promising in a wide range of applications. These materials are similar to stochastic foams which have found many industrial applications over the last few decades, but regular cellular structures possess a higher degree of control over the manufactured architectures made possible by additive manufacturing. These architected porous materials have properties that can be fine-tuned for a particular application (for mechanical performance, permeability, thermal properties, etc.). The control over the design and manufacturing of such architected structures in comparison to stochastic structures opens new application possibilities and enables a range of new products and features. This potential is only starting to be realized as metal AM techniques are maturing and are increasingly being adopted in various industries, and as design-for-AM capabilities improve. This review paper summarizes the unique properties of AM lattice structures and how these have been successfully employed for specific applications so far, and highlights various application areas of potential interest for the near future. The focus in this review paper is therefore on unique achievable properties and the associated applications for metal additively manufactured lattice structures.
... Introducing auxeticity into the tubular structure could further widen their application prospects [23]. Auxetic tubular structure exhibits improved impact energy absorption performance [24][25][26], thus could be used in the energy-absorbing device [27][28][29]. It also possesses superior bending performance [30,31] and interesting extension twist deformation response [32,33]. ...
Auxetic materials exhibit interesting deformation characteristics and excellent mechanical properties. A novel combined tubular structure with tunable stiffness is proposed in this work, aiming to improve the bearing capacity and stability by length design of the central column. Specimens were fabricated via 3D printing technique. Experimental test was performed to study their mechanical property and deformation characteristics under uniaxial compression. The validity of the finite element model was proved by comparing the experimental result with simulation prediction. The compression process and stress-strain curve of the tubular structure with tunable
stiffness exhibited four distinct stages (elastic, stiffness change, densification and buckling). Subsequently, a parametrical analysis was conducted to investigate the influences of the central connecting column on the stressstrain response, Poisson’s ratio and stability of the structure. By properly choosing the length of the central connecting column, the tubular structure could possess tunable stiffness, higher stability and compressive capacity. Furthermore, this design concept could be of benefit to the development of adaptive structures, smart devices and applications for civil engineering and protective engineering.
... In the case of consuming all stroke, i.e., when the tube "bottoms out", high peak loads emerge [5]. The high peak loads and violent fluctuations in loads increase the risk of whiplash [6]. To prevent this undesirable consequence and increase energy absorption capacity, auxetic materials have been considered [7]. ...
Our research investigated the energy absorption characteristics of chiral auxetic lattices filled cylindrical composite tubes subjected to a uniaxial and lateral quasi-static load. The lattice structures were manufactured using a 3D printing technique. Carbon fiber composite tubes without filler material were initially subjected to uniaxial and lateral quasi-static crushing load. The same types of experiment were then performed on chiral lattices and chiral lattices filled composite tubes. For the different cases, the load–displacements curves were analyzed and the specific energy absorption (SEA) values were compared. The SEA capability for the axial quasi-static crushing of the chiral lattices filled composite tubes decreased in comparison with the hollow composite design. However, the most significant result was that the average SEA value in the case of lateral loading increased dramatically in comparison with the hollow composite configuration.
... The whole bottom half of the defective empty tube are dominated by the X-shaped dentinduced plastic hinge ( Table 1). The collapse of the plastic hinge leads to a lower and much flatter stress plateau (0.10 < ε < 0.45, red curve in Fig. 2c), which is consistent with previously reported results [38,39]. When the curved and extended dent is in contact with the bottom cap at ε around 0.45 (Table 1), the tube stiffness increases. ...
Thin-walled structures have been widely used in automotive and aerospace industries to improve the system crashworthiness and impact protection. However, during manufacturing, transporting and handling processes, initial geometric imperfections are inevitably introduced to the thin-walled structures, which imposes negative impacts to the mechanical performance and service life of the thin-walled structures. In this study, we have introduced structural imperfection with controlled geometry and dimension to thin-walled steel tubes and characterized the mechanical response of these empty tubes and LN-filled tubes by quasi-static compression tests. Results show, the structural imperfection reduces the energy absorption capacity of empty tubes by about 20%. As the tube is filled with LN, the structural imperfection does not affect the energy absorption capacity of LN filled tube. The enhanced imperfection resistance is attributed to the suppression of imperfection growth caused by the strong liquid-solid interaction between the LN and tube wall. These findings suggest that the LN filling material can effectively reduce the adverse impact of structural imperfection and shed light on future design of thin-walled energy absorption devices.
... Lunhaizhi et al. (2018) has performed wind tunnel test and field measurements of wind loading on a super tall structure and found a fine agreement between the two results. Yang et al. (2017) has introduced the concept of predesigned ellipsoidal dimples into circular tubes and evaluated the impact of different design input parameters on it. ...
For the design of tubular structures, various researches have been inducted in past but still, there is no regulation made for providing the column spacing in the tube frame. This paper presents the comparison of four different types of a tubular structural frame with different spacing of columns in their periphery. The main objective of the research is to find an optimum spacing of columns in a tube frame without compromising the structural response. The columns are assigned at 7.5ft, 10ft, 15ft, and 30ft respectively in four tubular structures with the building height of 600 ft. Here the flat plate system has been used and its effect on the cost of the structure is observed. A simple linear static analysis is carried out and seismic loading has been applied in each model and their base shear and drifts were optimized by changing the column cross-section to get minimum steel ratio. Based on their total cost consumption and drift control, the most optimum and economical framing system has been concluded and a tube frame with 10 ft column spacing is recommended as the most suitable option for a symmetrical high-rise structure. Furthermore, these tubes were also get compared with a conventional moment resisting frame system, and all the analyzed tube frames are found to be more economical than a moment-resisting frame.
... A novel configuration with two concentric tubes connected with helically arranged stiffeners has been explored for a near-uniform crush force behaviour 37 . In the same category, circular tubes with ellipsoidal dimples have been studied to control the F peak and stabilize the crush force behaviour 38 . Cellular arrangement in 3D with a crush tube stiffened with plates arranged longitudinally at 90° to each other were attempted to reduce the fluctuations in the crush force behaviour 39 . ...
Crush tubes are used as crash impact energy absorbing structure (EAS) and are located in the frontal compartment of road vehicles. Ideal crashworthiness of an EAS mandates that the equivalent decelerations due to impact forces should to be ≤ 20g; and crush force and stroke efficiencies should tend to unity. It is understood from the literature that no single geometric cross-section shape exhibits a near-ideal crashworthiness; and most EAS members exhibit a high initial peak crush force which is detrimental to the occupant safety, and moderate stroke and crush force efficiencies leading to a compromise in the total energy absorbed. In this paper, finite element analysis (FEA) methodology is formulated and experimentally validated for axial crush of a crush tube of SS304 material with circular cross section. Subsequently, plastic deformation phenomenon and folding patterns in relation to crush force behaviour of crush tubes with various basic cross-sections of polygonal geometric shapes from triangle to octagon and circle are extensively studied through FEA. Further, two new geometric cross-section profiles with combination of basic shapes are proposed to combine the merits of different basic shapes. The crashworthiness of all basic cross-sections including the two proposed cross-section profiles is assessed based on standard parameters. The proposed new geometries may form a basis for the development of new EAS configurations for enhanced crashworthiness.
... Recently, Song et al. [21] and Yang et al. [33] investigated square and circular tubes with origami patterns. All of the results showed that these tubes performed better in terms of energy absorption with lower F max and higher F m compared to conventional tubes. ...
An origami crash box (OCB) has a desirable crashworthiness performance because it is inclined to deform in the diamond mode (DM) with a low initial peak force Fmax and high mean crushing force Fm. Theoretically, if an OCB whose shape approaches that of a conventional tube deforms in DM, the energy absorption will be the highest. Whereas, an OCB can deform in an undesirable incomplete diamond mode when its shape approaches that of a conventional tube. Additionally, the manufacture of OCBs is still complicated because it involves welding process. Therefore, a novel origami-ending tube (OET) is proposed in this paper. This OET was designed by introducing some small triangular origami patterns into the ends of the tube module, which greatly simplified the manufacturing process because it did not require welding. The validation experiments showed that the OET could deform in DM with a 46% reduction of Fmax and a 99% increase of Fm, compared to the conventional tube, even though the geometry of the OET was very close to that of a conventional tube. Combined with the results drawn from the validation experiments, parameters and comparison studies, it could be concluded that the OET performed better than the OCB.
... The whole bottom half of the defective empty tube are dominated by the X-shaped dentinduced plastic hinge ( Table 1). The collapse of the plastic hinge leads to a lower and much flatter stress plateau (0.10 < ε < 0.45, red curve in Fig. 2c), which is consistent with previously reported results [38,39]. When the curved and extended dent is in contact with the bottom cap at ε around 0.45 (Table 1), the tube stiffness increases. ...
... In fact, besides the above methods, there are many other ways to induce the tubes to deform in stable and progressive mode. Such as adding holes [26], grooves [27], tendons [28], corrugations [29][30][31][32] and origami features [33][34][35][36] on the wall, or diaphragms [37] and ribs [13,38] inside the tube. However, while these methods cause progressive deformation, they reduce the energy absorption efficiency. ...
... Generally, the shape of the slit of the auxetic tubular structure is predesigned. Recently, inspired by origami art and perforation techniques, many researchers create a variety of auxetic tubular structures with new perforation pattern design (Yang et al., 2016(Yang et al., , 2017. These perforated shapes are generally arranged in order. ...
Purpose
This paper aims to study the tensile performance, deformation characteristics, auxeticity and stability of different auxetic tubular structures generated by cutting method and pattern scale factor (PSF) method using validated finite element analysis.
Design/methodology/approach
Two types of auxetic tubular structures were designed by a coordinate transformation method and the PSF adjustment method, respectively. ABAQUS/explicit solver was used for the large deformation analysis and the displacement of key nodes was extracted to calculate Poisson’s ratio value and evaluate the deformation of tubular structures.
Findings
The random cut method was not suitable for designing auxetic tubular structures. Vertical and horizontal cut approach was suitable, but the change of the tubular diameter was lower than the tubular structures generated by the PSF adjustment method.
Research limitations/implications
Simple ways to generate auxetic tubular structure, which can be made into intelligent and foldable equipment, such as annuloplasty rings, angioplasty stents and oesophageal stents. By combined with shape memory polymer, various smart tubular materials and structures with various functions can be designed, especially in medical scaffold and other medical equipment fields.
Originality/value
The auxetic characteristic of tubular structure designed by using random cut method has been investigated for the first time. The outcome of this study would be very useful design tubular structures with better mechanical properties.
... Thin-walled structures are wildly used as energy absorption devices to protect the passengers and reduce the financial loss in the case of vehicle collisions [1]. Recently, considerable researches were conducted on the design of the thin-walled structures with complex geometry to achieve a higher energy absorption capacity, such as multi-cell tubes [2][3][4], dimpled tubular structures [5], functionally graded structures [6][7][8] and architected polymeric sandwich panels [9]. Complex manufacture process, such as wire cutting, and additive manufacturing technology, were employed to manufacture those structures, which significantly limits their real world application. ...
Cruciforms are frequently used as energy absorption components in engineering structures. The kirigami cru-ciforms (KCs) are designed by kirigami approach to simplify the manufacture process and reduce the initial peak force. However, the mean crushing force of KC is less than half of that of conventional cruciform (CC), which is negative for energy absorption purpose. The weak interaction between two component plates (plates A and B) in KC (no material connection) is a crucial factor for the decrease of mean crushing force. Therefore, laser welding technology is employed to enhance the connection between plates A and B by applying welding lines on the intersection line between components. Detailed analyses concerning the welding lines and boundary constraints are conducted to investigate the effect of connection between plates A and B. The results show that the mean crushing force of KC is close to that of CC if these conditions are met: the location of welding line is at the center of intersection line, and the length of welding line is no less than 30% and 43% of the length of cruciforms without and with symmetric boundary constraints on outside flanges, respectively. The conclusions indicate that the energy absorption capacity of thin-walled structure can be tuned by adjusting the connection strength between components in an energy absorption system.
... For a lower bound design, two equations were extracted from the results in order to generalise the response of such structures. Yang et al. (2017) designed and tested a dimpled body for tubes to obtain their energy absorption and they concluded that dimpled structures had a significantly reduced initial peak load compared with intact tubes. ...
This study was conducted using finite element analyses on CHS steel tubes with geometric variables. The ultimate capacity and buckling modes were evaluated and discussed in this paper. The effect of dent-shaped damages was assessed for different models with a varying slenderness, and the buckling behaviour was compared for such models. In general, the dent imperfection appeared to have a moderately reducing effect on the capacity. Yet, a reduction of 25% for the largest dents was found in slender models, which is significant when design and/or rehabilitation of these elements are taken into consideration. Very good agreement was seen comparing experiments and the present models demonstrating that the present FE approach was capable of being employed to examine the buckling response of dented cylindrical shells.
... They found that the patterned tubes exhibited a lower IPCF and more uniform crushing load compared with the conventional tubes. Yang et al. [18] introduced the pre-designed ellipsoidal dimples into the conventional circular tubes. They demonstrated that the dimpled tubes had substantially lower IPCF and remarkably less fluctuation in the crushing force than the conventional circular tubes. ...
In this study, a new tubular corrugated configuration mimicking the coconut tree profile, here named “conical corrugation tube” (CCT), was proposed, in an attempt to enhance the energy absorption, minimize the initial peak crushing force, and stabilize the crushing process. The effects of geometrical features, especially tapered angle and wavelength of CCTs on the deformation mode and energy absorption characteristics, were investigated through a series of numerical simulations. The results showed that the deformation modes of CCTs could be mainly classified into four modes, which were clearly influenced by the tapered angle and the wavelength of the CCTs. Moreover, the initial peak force of the CCTs was reduced significantly compared with that of the circular straight tube and the tapered tube. In addition, the undulation of the load-carrying capacity parameter, which is used to evaluate the stability of the crushing force, is minimized, and the CCTs produced smoother force-displacement curves compared with the circular straight tube and the tapered tube. Finally, a theoretical model was proposed to predict the mean crushing force of CCTs under dynamic impact loading. The theoretical results showed a good agreement with the numerical results.
... The fundamental principle of origami is to transform a flat sheet square (2-D) of paper into a finished sculpture (3-D) through folding and sculpting techniques along pre-defined creases. Because of its unique properties, origami has been imitated and developed to design foldable mechanisms ( Hanna et al., 2014), self-deployable structures (Delimont et al., 2015), robots (Jayaram and Full, 2016), self-folding structures ( Na et al., 2015), metamaterials ( Overbelde et al., 2017), energy absorbing structures ( Yang et al., 2016Yang et al., , 2017 and to solve plant structure folding (Couturier et al., 2013), soft matter folding ( Lin et al., 2016) and even protein folding problems (Gethin and Sambrook, 1992). From an engineering viewpoint, mechanical properties of the crease for designing origami structures are of significant importance, which should be fully understood and characterised. ...
In this study the mechanical behaviour of a creased thin strip under opposite-sense bending was investigated.
It was found that a simple crease, which led to the increase of the second moment of area, could
significantly alter the overall mechanical behaviour of a thin strip, for example the peak moment could be increased
by 100 times. The crease was treated as a cylindrical segment of a small radius. Parametric studies
demonstrated that the geometry of the strip could strongly influence its flexural behaviour. We showed that the
uniform thickness and the radius of the creased segment had the greatest and the least influence on the mechanical
behaviour, respectively. We further revealed that material properties could dramatically affect the overall
mechanical behaviour of the creased strip by gradually changing the material from being linear elastic to elasticperfect
plastic. After the formation of the fold, the moment of the two ends of the strip differed considerably
when the elasto-plastic materials were used, especially for materials with smaller tangent modulus in the plastic
range. The deformation patterns of the thin strips from the finite element simulations were verified by physical
models made of thin metal strips. The findings from this study provide useful information for designing origami
structures for engineering applications using creased thin strips.
Introducing origami patterns to the thin-walled tubes has been proven to effectively enhance the energy-absorbing capacity. However, the energy-absorbing capacity improved by pattern design alone has reached the ceiling and is difficult to improve further. In the present study, we provided a brand new technical route to solve this problem. We firstly designed a pre-folded thin-walled tube with uniform structure as the reference structure. We then made the wall thickness of the reference structure unhomogenized. Keeping the total mass of the tube unchanged, we thickened the wall thickness of the local region with relatively large plastic deformation, at the same time thinned the wall thickness of the local region with relatively small plastic deformation. Such non-uniform design makes the overall deformation of the thin-wall tube more harmonize, not only significantly increasing the specific energy absorption (SEA), but also decreasing the peak crushing force (PCF), achieving a superior combination of SEA and PCF.
Auxetic materials and structures have been attracting attention due to their extraordinary mechanical properties that stand out due to their high capacity to absorb energy. Some types of auxetic tubular structures have been studied and designed in diverse engineering fields such as mechanical, aerospace and medical. This manuscript cites more than a hundred papers containing the definitions, designs, structural analyses and optimization, mechanical properties, and specific applications of tubular design of auxetic structures. It can be noted from the present paper that additive manufacturing has been one of the most common manufacturing techniques used in many cases to manufacture tubular structures, and numerical analysis was essential to analyzing the behavior of the structures. The purpose of this paper is to assist researchers and engineers in using the methodology step by step to develop and apply auxetic tubular structures.
Textured pipe has been proposed to improve the propagation buckling capacity of subsea pipelines recently. Due to its special geometry, textured pipe may have the potential to mitigate the vortex induced vibration (VIV) by altering the wake vortex street formation. In the present study, the effectiveness of using a full-diamond textured pipe for VIV suppression is numerically investigated in a coupled fluid-structure interaction (FSI) framework. Three-dimensional (3D) Computational Fluid Dynamics (CFD) analyses are performed by using the Reynolds-Averaged Navier-Stokes (RANS) turbulence model equipped with shear stress transport (SST)K−ω model at the subcritical Reynolds numbers (Re) with Re∈[2000,12000]. The results are compared in detail with an equivalent conventional smooth cylinder subjected to the same flow conditions. Numerical results show that the textured cylinder can significantly mitigate the undesired VIV and the associated hydrodynamic forces. It eliminates the upper excitation regime in the conventional smooth cylinder and the width of the synchronization regime is also remarkably reduced.
The bumper systems (beams and face bars) are parts of the car body structure, one of the most important components of an auto vehicle because of its role in absorbing the energy of an impact by deformation. The main objective of this paper is to study, optimize the built shape of the frontal members beams used in the endurance structure of motor vehicles in terms of their ability to absorb internal energy resulting from a frontal impact under the principles of sustainability. The study combines the classical technology used in the construction of vehicles with, the Origami Engineering” technique, which is generally used by NASA, but also by engineers in other fields: aeronautics, nanotechnology or medical technique. Simulation analyses were performed using the finite element on different types of thin-walled metal tubes, but also an origami structure.
The Radio Frequency Identification (RFID), is a wireless technology system that is used for identifying an individual or objects through the means of radio waves which transfer information from an electronic tag, called Radio Frequency Identification (RFID) tag. Radio Frequency Identification (RFID) consists of two main components the interrogator and the transponder. The Interrogator, which is the Radio Frequency identification reader (RFID Reader), the Interrogator usually transmits and receives the signal while the Transponder (tag) is attached to the object. In the Radio Frequency Identification (RFID) system, an RFID reader interrogates the Radio Frequency Identification (RFID) tags. This tag reader generates a radio frequency interrogation, which communicates with the tags been registered in the system. This reader likewise has a receiver that captures a reply signal generated from the tags and decodes the signal. This reply signal from the tags reflects the tag's information content. Each tag of the students consists of a unique identity, identification card (ID) that is assigned to a single student identification card (ID) which is recorded in the database. The use of the Radio Frequency Identification (RFID) technology enables the institution authorities or management to evade attendance documents from damages such as misplacement, tear, or even got lost. This research review some recent design and implementation of internet of things (IoT) attendance system using the concept of the Radio Frequency Identification (RFID) system articles. The analysis found that the Radio Frequency Identification (RFID) system is a very advanced technology for an automatic attendance system in an institution, organization, or university and it provides a very higher performance and accuracy than the traditional paper-based system that the students normally used to sign. A combination of the model is needed which will confirm higher security, better performance, and consistency of the system.
Thin-walled square tubes are widely used as impact energy absorber in automotive structures due to their ease of fabrication and installation, high energy absorption capacity in terms of progressive plastic deformation and long stroke. However, the main drawback of square tube is its high initial peak force during the initial stage of crushing. An origami pattern on the faces of the tube is proposed to reduce the high initial peak force and increase the energy absorption of the tube. Static and dynamic axial crushing were performed using finite element analysis to determine the initial peak force (IPF), crush force efficiency (CFE) and plastic specific energy absorption (SEA) of tubes with origami pattern. The results of simulations were validated by experimental data. Then, various combinations of origami patterns were studied using finite element simulation only. It was found that the origami pattern significantly enhanced the tubes crush performance. Comparison between plain square tube and tubes with various origami patterns was carried out and it was found that the origami patterns reduced the initial peak force and increased the crush force efficiency for both static and dynamic loading conditions.
A novel origami-ending tube, which features the origami patterns at the ends, can deform in the diamond mode with an outstanding energy absorption performance. However, many quasi-static axial crushing experimental results showed that the long origami-ending tubes with two modules could deform in the corner symmetric mode and the mixed mode. Thus the SEAs were reduced by up to 38% and 25% compared to the diamond mode. The experimental and numerical results revealed that the local buckling and the initial concave imperfections were the main reasons triggering the corner symmetric mode and the mixed mode, respectively. The imperfection analysis indicated that the opposite local buckling imperfection and opposite concave imperfection had the greatest influence on the collapse mode and the SEA. Therefore, the reinforced metal sheets and slight convex creases were introduced into the tube to reduce the imperfection sensitivity and to improve the stability of deformation. Numerical simulations and quasi-static experiments validated that the performances of the reinforced tubes had been greatly improved in terms of energy absorption and imperfection resistance. Additionally, a simple manufacturing process was proposed, which is hopeful to achieve the mass production of long origami-ending tube.
A high-efficient energy absorption design in virtue of ultrasonic impact surface nanocrystallization treatment is proposed to enhance the crashworthiness of square thin-walled tubes. Due to significant improvement on mechanical characteristics within the treated areas, structural crashworthiness after surface nanocrystallization is significantly increased without the requirement of modifying configurations or mass. The results reveal that by optimizing local surface nanocrystallization layouts with a nanocrystallization area treatment ratio of approximately 50%, the specific energy absorption is enhanced by 64.29% as compared to the untreated tube. Experimental study validates that this technology is effective in the enhancement of the crashworthiness of square thin-walled tubes.
The paper presents the results of numerical tests of impact and energy absorption capacity of thin-walled columns, subjected to axial impact loading, made of aluminum alloy, and having a square cross-section and spherical indentations on their lateral surfaces. The numerical models were validated using an experiment that was conducted on the Instron CEAST 9350 High Energy System drop hammer. Material properties of the applied aluminum alloy were determined on the basis of a static tension test. The crushing behavior of the columns and some crashworthiness indicators were investigated. On the basis of the results of the conducted analyses, conclusions were drawn about the most beneficial design/constructional variants in terms of achieved crashworthiness parameters.
Helicopters are versatile aircraft that can perform numerous missions such as ground surveillance, rescue missions, air ambulance, fire-fighting etc. However, helicopter crashes sometimes occur owing to technical failures or human errors. Accordingly, the crashworthy design of helicopters has always remained a top priority to prevent catastrophic structural failure and significant casualties. The crashworthy performance of helicopters can be immensely improved with well-designed energy absorption materials or structures. This paper presents a systematic literature review on crashworthy design and energy absorption mechanisms for helicopter structures. Firstly, the historical development of aircraft crashworthiness investigation at various periods over the past few decades is presented. Then, some typical energy absorbing components such as rings, tubes, honeycombs, corrugated structures and emerging energy absorbers are introduced to act as the major structural elements for the crashworthy design of helicopters. After that, an emphasis is placed on the dynamic behavior and energy absorption of typical helicopter structures such as the landing gear, subfloor, full-scale airframe, helicopter crashworthy seats, fuel tank and helicopter blade. In addition, representative helicopter crash scenarios such as bird strike, water impact and the impact response and injury of the occupants are described. Finally, the crashworthy evaluation criteria of helicopter structures are summarized in this paper. This article is intended as a comprehensive literature review of crashworthy design and impact protection of helicopter structures.
An experimental and numerical study on the quasi-static loading of AlSi10Mg square boxes produced by selective laser melting (SLM) was carried out. The goal was to evaluate the applicability of common finite element modelling techniques to 3D-printed parts at material and component scales, under large deformations and fracture. Uniaxial tensile specimens were extracted and tested at different orientations, and a hypo-elastic–plastic model with Voce hardening and Cockcroft–Latham’s fracture criterion was calibrated against the experimental results. The boxes were crushed laterally until failure using a spherical actuator. The considered material and finite element models were proved well suited for the prediction of the structural response of the additively manufactured components in the studied scenario.
Honeycomb structures have been extensively employed as energy absorption devices. This paper proposes a kind of energy absorption structure known as the pre-folded honeycomb, which is made from conventional honeycomb with a pre-folded trace. The folding mode and energy absorption performance of the pre-folded structure under in-plane impact load were investigated both numerically and experimentally. Furthermore, the response surface method was chosen to find the optimal pre-folded honeycomb structure for the purpose of maximizing the specific energy absorption. The results demonstrate that the proposed method is effective in solving crashworthiness design-optimization problems. Additionally, the numerical results show that the in-plane structural strength of pre-folded honeycomb is nearly 8 times higher than that of conventional honeycomb.
The paper presents results of the numerical and experimental study into crashworthiness performance and energy absorption capability of thin-walled square section columns with dents, subjected to axial impact load. Thin-walled aluminum tubes with four dents in the corners are under investigation. Energy absorption effectiveness of energy absorbing thin-walled structures is discussed. Finite Element parametric study into energy absorption capacity of structures under investigation is performed. Crushing behavior and some crashworthiness indicators are examined. Results of experimental impact tests carried out on aluminum tubes with dents of selected shape and position are presented. FE theoretical model and numerical results are confronted with those obtained from experimental tests. Some conclusions concerning optimal dent shape and position are derived.
Designing metamaterials with programmable features has emerged as a promising pathway for reusable energy absorption. While the current designs of reusable energy absorbers mainly exploit mechanical instability of flexible beams, here is created a new kind of metamaterial for reusable and programmable energy absorption by integrating rigid granular materials and compliant stretchable components. In each unit cell of the metamaterial, the stretchable components connect the granular particles to maintain the integrity and control the deformation pattern of the material. When the metamaterial is subjected to an external load, the input energy is partially trapped as elastic energy in the stretchable components, and partially dissipated by friction between the granular particles, forming hysteresis between the loading and unloading force–displacement curves. Through tuning the structural design of the metamaterial, the pretension and stiffness of the stretchable components, and the size of and friction between the particles, a vast design space is achieved to program the mechanical behavior of the metamaterial, such as the load–displacement curve, the multistability, and the amount of energy dissipation. Experimental impact tests on a thin glass panel confirm energy‐absorbing capability of the proposed metamaterial. This design strategy opens a new avenue for creating reusable energy‐absorbing metamaterials.
Thin-walled tubes subjected to axial crushing have been extensively employed as energy absorption devices in transport vehicles. Conventionally, they have a square or rectangular section, either straight or tapered. Dents are sometimes added to the surface in order to reduce the initial buckling force. This paper presents a novel thin-walled energy absorption device known as the origami crash box that is made from a thin-walled tube of square cross section whose surface is prefolded according to a developable origami pattern. The prefolded surface serves both as a type of geometric imperfection to lower the initial buckling force and as a mode inducer to trigger a collapse mode that is more efficient in terms of energy absorption. It has been found out from quasi-static numerical simulation that a new collapse mode referred to as the completed diamond mode, which features doubled traveling plastic hinge lines compared with those in conventional square tubes, can be triggered, leading to higher energy absorption and lower peak force than those of conventional ones of identical weight. A parametric study indicates that for a wide range of geometric parameters the origami crash box exhibits predictable and stable collapse behavior, with an energy absorption increase of 92.1% being achieved in the optimum case. The origami crash box can be stamped out of a thin sheet of material like conventional energy absorption devices without incurring in-plane stretching due to the developable surface of the origami pattern. The manufacturing cost is comparable to that of existing thin-walled crash boxes, but it absorbs a great deal more energy during a collision.
A series of over 120 axial crushing tests were conducted on circular and square steel tubes loaded either statically or dynamically. Approximate theoretical predictions for static and dynamic progressive buckling are developed. Fair agreement with the experimental results is achieved provided the effective crushing distance is taken into account and the infuence of material strain rate sensitivity is retained for dynamic loads.
Thin-walled structures are widely used as energy absorbing devices for their proven advantages on lightweight and crashworthiness. However, conventional thin-walled structures often exhibit unstable collapse modes and excessive initial peak crushing force (IPCF) followed by undesirable fluctuation in force-displacement curves under impact loading. This paper introduces a novel tubal configuration, namely sinusoidal corrugation tube (SCT), to control the collapse mode, and minimize the IPCF and fluctuations. Through validating the finite element (FE) models established, the effects of wavelength, amplitude, thickness and diameter of SCTs on collapse mode and energy absorption were investigated. The results showed that SCTs can make the deformation mode more controllable and predictable, which can be transformed from a mixed mode to a ring mode by simply changing the wavelength and amplitude. Compared with the traditional straight circular tube, the IPCF is reduced appreciably. Furthermore, SCTs have lower fluctuation in the force-displacement curves than traditional straight circular tubes. Finally, a multiobjective optimization is conducted to obtain the optimized SCT configuration for maximizing specific energy absorption (SEA), minimizing IPCF under the constraint of fluctuation criterion. The optimal SCTs are of even more superior crashworthiness and great potential as an energy absorber.
Thin-walled tubes are widely used as energy absorption components. In this study, two different origami
patterns were introduced to circular tubes. The influence of the origami patterns on the energy absorption capacity and the deformation mechanism of tubes under uniaxial loading were investigated
both numerically and experimentally. The results showed that the initial peak force of origami tubes
would be significantly reduced, while the energy absorption capacity could be improved or maintained.
Brass tubes with and without origami patterns were fabricated using 3D printing and were tested to
validate the finite element models.
This paper presents a novel thin-walled tube design with a pre-folded kite-shape rigid origami pattern as an energy absorption device. Numerical simulation of the quasi-static axial crushing of the new device shows that a smooth and high reaction force curve can be achieved in comparison with those of conventional square tubes, with an increase of 29.2% in specific energy absorption and a reduction of 56.5% in initial peak force being obtained in the optimum case. A theoretical study of the energy absorption of the new device has also been conducted, which matches reasonably well with the numerical results.
This important study focuses on the way in which structures and materials can be best designed to absorb kinetic energy in a controllable and predictable manner. Understanding of energy absorption of structures and materials is important in calculating the damage to structures caused by accidental collision, assessing the residual strength of structures after initial damage and in designing packaging to protect its contents in the event of impact. Whilst a great deal of recent research has taken place into the energy absorption behaviour of structures and materials and significant progress has been made, this knowledge is diffuse and widely scattered. This book offers a synthesis of the most recent developments and forms a detailed and comprehensive view of the area. It is an essential reference for all engineers concerned with materials engineering in relation to the theory of plasticity, structural mechanics and impact dynamics. © 2003 Woodhead Publishing Limited Published by Elsevier Ltd All rights reserved.
Inextensional collapse modes are presented for the axial compression of thin-walled tubes. Shortening is achieved by folding about fixed hinge lines to form a number of flat triangular planes. A new mechanism is propounded by which collapse proceeds progressively from one end of the tube, following the passage of a travelling hinge.
Simple expressions are developed for mean collapse load and the energy absorbed during collapse of rigid-perfectly plastic tubes.
Comparison of collapse modes and predicted loads with those obtained from experiments on rigid P.V.C. tubes of various thickness, diameter and length give encouraging agreement.
A series of axial crushing tests on steel circular cylindrical shells loaded either statically or dynamically is reported and compared with various theoretical predictions and empirical relations. A modified version of Alexander's theoretical analysis for axisymmetric, or concertina, deformations gives good agreement with the experimental results when the effective crushing distance is considered and provided that the influence of material strain rate sensitivity is retained in the dynamic crushing case.
An approximate theory for the process is derived, leading to a solution of the type P = Ct1.5√D, where P is the collapse load, t the shell thickness, D the shell diameter, and C a constant for any given material. Good
agreement is exhibited between this relationship and experimental results.
Similar to the concertina mode, the wall of axially crushed tubes deforming in multi-lobe or diamond mode, will be laid down partly to the inside and partly to the outside of the tube generator with the latter part being smaller than the former. Such proportion of the folding length is known as the eccentricity factor, in both the concertina and multi-lobe modes. The present work examines the collapse of tubes in the multi-lobe in an attempt to evaluate the crushing load using this unique factor. The analysis produced a distinctive value for the eccentricity factor that simplifies the expression for the mean collapse load, which is a function of tube geometry and number of lobes. The analytical outcome for the mean crushing load, the total deflection is in a reasonable agreement with those obtained from experiment. Furthermore, the measured values of the eccentricity factor and the critical folding angles obtained for tubes of different materials and geometric ratios are also in good agreement with those produced by the analysis which postulates that the distinctive value of m is independent of the tube’s material and geometric ratios.
This paper examines the effective crushing distance of thin-walled box columns. In contrast to previous work on this subject where a perfectly plastic material was assumed, the hardening property of a material is now taken into account. A simplified theoretical model of a compressed rigid-linearly strain hardening metal strip is studied and a closed-form solution is derived for the crushing distance of unstiffened as well as transversly stiffened box columns. The theoretical predictions are in excellent agreement with experimental data.
This paper presents further experimental investigations into axial compression of thin-walled circular tubes, a classical problem studied for several decades. A total of 70 quasi-static tests were conducted on circular 6060 aluminium tubes in the T5, as-received condition. The range of D/t considered was expanded over previous studies to D/t=10–450. Collapse modes were observed for L/D⩽10 and a mode classification chart developed. The average crush force, FAV, was non-dimensionalised and an empirical formula established as FAV/MP=72.3(D/t)0.32. It was found that test results for both axi-symmetric and non-symmetric modes lie on a single curve. Comprehensive comparisons have been made between existing theories and our test results for FAV. This has revealed some shortcomings, suggesting that further theoretical work may be required. It was found that the ratio of FMAX/FAV increased substantially with an increase in the D/t ratio. The effect of filling aluminium tubes with different density polyurethane foam was also briefly examined.
The results of an experimental investigation of the axial crushing modes and energy absorption properties of quasi-statically compressed aluminium alloy tubes are presented. In particular, the influence of tube length on these properties is discussed and quantified and a classification chart presented. This chart together with other experimental data, enables a designer to predict the energy absorbing properties of a given tube as well as its mode of crushing.
The energy absorption characteristics of corrugated tubes are experimentally studied. The corrugations are introduced in the tube to force the plastic deformation to occur at predetermined intervals along the tube generator. The aims are to improve the uniformity of the load—displacement behaviour of axially crushed tubes, predict and control the mode of collapse in each corrugation in order to optimize the energy absorption capacity of the tube. Effect of heat treatment and foam filling of these tubes are also considered. Metal tubes are mostly used throughout this study, however, PVC tubes are also considered for comparison purposes. The experimental results of crushing of the corrugated tubes make these tubes a good candidate for a controllable energy absorption element.
An extensive experimental database has been established for the structural behaviour of aluminium foam and aluminium foam-based components (foam-filled extrusions). The database is divided into three levels, these are: (1) foam material calibration tests, (2) foam material validation tests and finally (3) structural interaction tests where the foam interacts with aluminium extrusions. This division makes it possible to validate constitutive models applicable to aluminium foam for a wide spectrum of loading configurations. Several existing material models for aluminium foam from the literature are discussed and compared. To illustrate the use of the database, four existing material models for foams in the explicit, non-linear finite element code LS-DYNA have been calibrated and evaluated against configurations in the database.
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K. Yang et al.
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