Project

Multi-scale Optimisation for Additive Manufacturing of fatigue resistant shock-absorbing MetaMaterials — MOAMMM

Goal: Develop a data-driven design methodology for mechanical components made of metamaterials and produced by additive manufacturing

Design, 2-scale optimisation and process optimisation of shock-absorption devices

Targeted applications: shock-absorption devices

www.moammm.eu

Date: 1 January 2020 - 31 December 2023

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Lucia Cobian
added a research item
Selective laser sintering (SLS) of polymers has made possible the introduction of lattice-based cells as building blocks of polymer parts, allowing to obtain optimal specific properties. The actual mechanical performance of an SLS part is strongly dependent on the printing direction and part shape. Nevertheless, macroscopic testing is not usually possible due to size restrictions of the fabricated part, as it happens, for example, in lattice-based materials. In this case, microscopic tests performed directly on the lattice surface become fundamental. In this work, the mechanical behavior of SLS PA12 under a wide range of strain rates from 10⁻³ to 10³ s⁻¹ and different printing directions is characterized using macroscopic tests on bulk samples and compared with nanoindentation performed directly on the lattice material surface. An excellent correlation was found between the rate-dependent mechanical behavior obtained at the two scales, validating microscopic techniques for characterizing the mechanical response of SLS fabricated PA12 parts.
Issam Doghri
added a research item
An efficient modeling procedure is proposed for viscoelastic (VE) solids subjected to large numbers of loading cycles. While the Laplace-Carson transform (LCT) is often used to solve VE creep or relaxation problems, the originality here is an efficient extension of the approach to a plethora of cycles, based on some key ingredients. The time history of the cyclic loading is decomposed into transient and periodic signals, leading to two subproblems. Each one is transformed into a finite number of linear elastic analyses in the L-C domain. A method to choose the number and positioning of the L-C domain sampling points for each one of the two subproblems is detailed. Specific LCT inversion methods are applied to each subproblem in order to reconstruct the displacement, strain and stress fields in the time domain. For the transient subproblem, Schapery's collocation method based on exponential basis functions is used, while a new LCT inversion method is proposed for the periodic subproblem based on sinusoidal basis functions and a Newton-Gauss algorithm. After a verification on well-known 1D functions, the accuracy of the proposed method is assessed on two structural problems with large numbers of cycles. Comparison with reference finite element analyses conducted directly in the time domain shows that the proposed methodology provides excellent predictions, both at local scale (displacement, strain and stress components at various points) and macroscale (global energy indicator). The important speedup factor (e.g., 32 for 10k cycles) will increase significantly with the number of cycles, enabling the proposed method to be extended to high cycle fatigue of thermoplastic polymer structures in future work. KEYWORDS Laplace-Carson numerical inversion, high cycle simulation, periodic basis extension, viscoelastic structure.
Javier Segurado
added a research item
We present a computational homogenization study on the particle size effect in ductile composites. The micromechanical formulation is based on non-local models through (i) the incorporation of a lower-order strain gradient plasticity model and (ii) the application of an implicit gradient regularization technique to the Gurson-Tvergaard-Needleman ductile damage model for metals. In this way, the extended model is equipped with two length-scale parameters, one for each non-local extension, which modulate the size dependent character of the formulation. The problem consists of a system of partial differential equations in which two Helmholtz-type equations for the damage regularization are coupled with the balance of linear momentum through the stress, which depends on the non-local variables and on the plastic strain gradient. A series of numerical simulations are conducted to investigate the behavior of three-dimensional microstructures representative of particle reinforced metal matrix composites. The change in strengthening and ductility, as a function of the particle size, is first analyzed by means of a parametric study in which the considered non-local extensions act both independently and together. Finally a comparative study with experimental results demonstrates that the particle size induced strengthening in metal matrix composites can be quantitatively captured by the considered model.
Anna Hössinger-Kalteis
added a research item
The selective laser sintering (SLS) is an additive manufacturing technology with clear potential for producing high quality polymeric components of various thermoplastic polymers and elastomers which can be used in demanding engineering applications under complex service loading conditions. The prerequisite for these applications is that the stiffness and the tensile strength of the SLS specimens is in the same range as for injection molded specimens using a proper parameter set of the SLS process and qualified materials. While the tensile strength of SLS printed polymers is recently determined by many researchers, hardly any data are available about the fatigue behavior of SLS polymers on specimen level and even less on component level. Cylindrical specimens with and without round notch have been designed and additively manufactured using PA12 and TPU SLS grades in two different printing directions (vertical and horizontal). The monotonic tensile behavior was characterized over a wide loading rate range (0.1 to 100 mm/s) and the tensile strength and failure strain values were determined. The fatigue behavior was characterized under cyclic loading conditions at various stress ratios (R=0.1, -1), at a constant frequency of 5 Hz at 5 stress levels. Stress vs. cycle number-to-failure, Nf points were determined for constructing conventional S-N curves for the materials investigated. A distinct anisotropy of the tensile strength and failure strain was recognized for the SLS TPU investigated.
Ludovic Noels
added a research item
Artificial Neural Networks (NNWs) are appealing functions to substitute high dimensional and non-linear history-dependent problems in computational mechanics since they offer the possibility to drastically reduce the computational time. This feature has recently been exploited in the context of multi-scale simulations, in which the NNWs serve as surrogate model of micro-scale finite element resolutions. Nevertheless, in the literature, mainly the macro-stress–macro-strain response of the meso-scale boundary value problem was considered and the micro-structure information could not be recovered in a so-called localization step. In this work, we develop Recurrent Neural Networks (RNNs) as surrogates of the RVE response while being able to recover the evolution of the local micro-structure state variables for complex loading scenarios. The main difficulty is the high dimensionality of the RNNs output which consists in the internal state variable distribution in the micro-structure. We thus propose and compare several surrogate models based on a dimensionality reduction: (i) direct RNN modeling with implicit NNW dimensionality reduction, (ii) RNN with PCA dimensionality reduction, and (iii) RNN with PCA dimensionality reduction and dimensionality break down, i.e. the use of several RNNs instead of a single one. Besides, we optimize the sequential training strategy of the latter surrogate for GPU usage in order to speed up the process. Finally, through RNN modeling of the principal components coefficients, the connection between the physical state variables and the hidden variables of the RNN is revealed, and exploited in order to select the hyper-parameters of the RNN-based surrogate models in their design stage.
Javier Segurado
added a research item
FFT methods have become a fundamental tool in computational micromechanics since they were first proposed in 1994 by H. Moulinec and P. Suquet for the homogenization of composites. From that moment on many dierent approaches have been proposed for a more accurate and efficient resolution of the non- linear homogenization problem. Furthermore, the method has been pushed beyond its original purpose and has been adapted to many other problems including continuum and discrete dislocation dynamics, multi-scale modeling or homogenization of coupled problems as fracture or multiphysical problems. In this paper, a comprehensive review of FFT approaches for micromechanical simulations will be made, covering the basic mathematical aspects and a complete description of a selection of approaches which includes the original basic scheme, polarization based methods, Krylov approaches, Fourier-Galerkin and displacement-based methods. The paper will present then the most relevant applications of the method in homogenization of composites, polycrystals or porous materials including the simulation of damage and fracture. It will also include an insight into synergies with experiments or its extension towards dislocation dynamics, multi-physics and multi-scale problems. Finally, the paper will analyze the current limitations of the method and try to analyze the future of the application of FFT approaches in micromechanics.
Issam Doghri
added a research item
This paper deals with the micromechanical modeling of polymer composites with viscoelastic-viscoplastic (VE-VP) constituents. Two mean-field homogenization (MFH) models based on completely dissimilar theoretical approaches are extended from elasto-viscoplasticity (EVP) to VE-VP and assessed. The first approach is the incremental-secant method. It relies on a fictitious unloading of the composite at the beginning of each time step. Then, a thermoelastic-like Linear Comparison Composite (LCC) is constructed from the computed residual state directly in the time domain. The method provides naturally isotropic per-phase incremental-secant operators for isotropic VE-VP constituents. It takes into account both the first and the second statistical moment estimates of the equivalent stress micro-field. The second approach is the integral affine method. It starts by linearizing the rates of viscoplastic strain and internal variables. The linearized constitutive equations are then recast in a hereditary integral format to which the Laplace-Carson (L-C) transform is applied. A thermoelastic-like LCC is built in the L-C domain, where MFH is carried out. Finally, the composite's response in the time domain is recovered by numerical inversions of L-C transforms. The method is able to overcome the issue of heterogeneous viscous stresses encountered by time domain MFH models. The two proposed MFH formulations are able to handle non-monotonic, non-proportional and multi-axial loading histories. Their accuracy was assessed against full-field finite element (FE) results for different microstructures and loadings. The computational cost of both methods is negligible compared to FE analyses. Overall, the incremental-secant approach is much simpler mathematically and numerically than the integral affine formulation, its accuracy ranges from acceptable to excellent, and important improvements can be expected in the future by controlling the virtual unloading time increment.
Javier Segurado
added a research item
An FFT framework which preserves a good numerical performance in the case of domains with large regions of empty space is proposed and analyzed for its application to lattice based materials. Two spectral solvers specially suited to resolve problems containing phases with zero stiffness are considered (1) a Galerkin approach combined with the MINRES linear solver and a discrete differentiation rule and (2) a modification of a displacement FFT solver which penalizes the indetermination of strains in the empty regions, leading to a fully determined equation. The solvers are combined with several approaches to smooth out the lattice surface, based on modifying the actual stiffness of the voxels not fully embedded in the lattice or empty space. The accuracy of the resulting approaches is assessed for an octet-lattice by comparison with FEM solutions for different relative densities and discretization levels. It is shown that the adapted Galerkin approach combined with a Voigt surface smoothening was the best FFT framework considering accuracy, numerical efficiency and h-convergence. With respect to numerical efficiency it was observed that FFT becomes competitive compared to FEM for cells with relative densities above ≈7%. Finally, to show the real potential of the approaches presented, the FFT frameworks are used to simulate the behavior of a printed lattice by using direct 3D tomographic data as input. The approaches proposed include explicitly in the simulation the actual surface roughness and internal porosity resulting from the fabrication process. The simulations allowed to quantify the reduction of the lattice stiffness as well as to resolve the stress localization of ≈ 50% near large pores.
Javier Segurado
added 3 research items
The simulation of fracture using continuum ductile damage models attains a pathological discretization dependence caused by strain localization, after loss of ellipticity of the problem, in regions whose size is connected to the spatial discretization. Implicit gradient techniques suppress this problem introducing some inelastic non-local fields and solving an enriched formulation where the classical balance of linear momentum is fully coupled with a Helmholtz-type equation for each of the non-local variable. Such Helmholtz-type equations determine the distribution of the non-local fields in bands whose width is controlled by a characteristic length, independently on the spatial discretization. The numerical resolution of this coupled problem using the Finite Element method is computationally very expensive and its use to simulate the damage process in 3D multi-phase microstructures becomes prohibitive. In this work, we propose a novel FFT-based iterative algorithm for simulating gradient ductile damage in computational homogenization problems. In particular, the Helmholtz-type equation of the implicit gradient approach is properly generalized to model the regularization of damage in multi-phase media, where multiple damage variables and different characteristic lengths may come into play. In the proposed iterative algorithm, two distinct problems are solved in a staggered fashion: (i) a conventional mechanical problem via a FFT-Galerkin solver with mixed macroscopic loading control and (ii) the generalized Helmholtz-type equation using a Krylov-based algorithm combined with an efficient pre-conditioner. The numerical implementation is firstly validated on simple two-dimensional microstructures, showing identical responses for different spatial discretizations and reproducing a ductility change dependent on the characteristic length. Finally, the robustness and efficiency of the algorithm is demonstrated in the simulation of failure of complex 3D particle reinforced composites characterized by millions of degrees of freedom.
An FFT framework which preserves a good numerical performance in the case of domains with large regions of empty space is proposed and analyzed for its application to lattice based materials. Two spectral solvers specially suited to resolve problems containing phases with zero stiffness are considered (1) a Galerkin approach combined with the MINRES linear solver and a discrete differentiation rule and (2) a modification of a displacement FFT solver which penalizes the indetermination of strains in the empty regions, leading to a fully determined equation. The solvers are combined with several approaches to smooth out the lattice surface, based on modifying the actual stiffness of the voxels not fully embedded in the lattice or empty space. The accuracy of the resulting approaches is assessed for an octet-lattice by comparison with FEM solutions for different relative densities and discretization levels. It is shown that the adapted Galerkin approach combined with a Voigt surface smoothening was the best FFT framework considering accuracy, numerical efficiency and h-convergence. With respect to numerical efficiency it was observed that FFT becomes competitive compared to FEM for cells with relative densities above ≈7%. Finally, to show the real potential of the approaches presented, the FFT frameworks are used to simulate the behavior of a printed lattice by using direct 3D tomographic data as input. The approaches proposed include explicitly in the simulation the actual surface roughness and internal porosity resulting from the fabrication process. The simulations allowed to quantify the reduction of the lattice stiffness as well as to resolve the stress localization of ≈ 50% near large pores.
The simulation of fracture using continuum ductile damage models attains a pathological discretization dependence caused by strain localization, after loss of ellipticity of the problem, in regions whose size is connected to the spatial discretization. Implicit gradient techniques suppress this problem introducing some inelastic non-local fields and solving an enriched formulation where the classical balance of linear momentum is fully coupled with a Helmholtz-type equation for each of the non-local variable. Such Helmholtz-type equations determine the distribution of the non-local fields in bands whose width is controlled by a characteristic length, independently on the spatial discretization. The numerical resolution of this coupled problem using the Finite Element method is computationally very expensive and its use to simulate the damage process in 3D multi-phase microstructures becomes prohibitive. In this work, we propose a novel FFT-based iterative algorithm for simulating gradient ductile damage in computational homogenization problems. In particular, the Helmholtz-type equation of the implicit gradient approach is properly generalized to model the regularization of damage in multi-phase media, where multiple damage variables and different characteristic lengths may come into play. In the proposed iterative algorithm, two distinct problems are solved in a staggered fashion: (i) a conventional mechanical problem via a FFT-Galerkin solver with mixed macroscopic loading control and (ii) the generalized Helmholtz-type equation using a Krylov-based algorithm combined with an efficient pre-conditioner. The numerical implementation is firstly validated. Finally, the robustness and efficiency of the algorithm is demonstrated in the simulation of failure of complex 3D particle reinforced composites characterized by millions of degrees of freedom.
Ludovic Noels
added a research item
Compared to conventional projection-based model-order-reduction, its neural-network acceleration has the advantage that the online simulations are equation-free, meaning that no system of equations needs to be solved iteratively. Consequently, no stiffness matrix needs to be constructed and the stress update needs to be computed only once per increment. In this contribution, a recurrent neural network is developed to accelerate a projection-based model-order-reduction of the elastoplastic mechanical behaviour of an RVE. In contrast to a neural network that merely emulates the relation between the macroscopic deformation (path) and the macroscopic stress, the neural network acceleration of projection-based model-order-reduction preserves all microstructural information, at the price of computing this information once per increment.
Hans Nopper
added a research item
Computer-assisted surgery and the use of virtual environments in surgery are getting popular lately, as they provide numerous benefits, especially for visualisation of data. Yet, these tools lack features for direct and interactive discussion with remote experts and intuitive means of control for 3D data. Therefore, we present a concept to create an immersive multi-user system, by using virtual reality, augmented reality and 3D-printed organ models, which enables a collaborative workflow to assist surgeries. The 3D models will be an interaction medium to provide haptic feedback as well as teaching material. Additionally, multiple depth cameras will be used to provide remote users in the virtual environment with a realistic live representation of the operating room. Our system can be used in the planning stage, intraoperatively as well as for training. First prototypes were rated as highly useful by visceral surgeons in a focus group.
Ludovic Noels
added a project goal
Develop a data-driven design methodology for mechanical components made of metamaterials and produced by additive manufacturing
Design, 2-scale optimisation and process optimisation of shock-absorption devices
Targeted applications: shock-absorption devices
 
Ludovic Noels
added a research item
An artificial Neural Network (NNW) is designed to serve as a surrogate model of micro-scale simulations in the context of multi-scale analyses in solid mechanics. The design and training methodologies of the NNW are developed in order to allow accounting for history-dependent material behaviors. On the one hand, a Recurrent Neural Network (RNN) using a Gated Recurrent Unit (GRU) is constructed, which allows mimicking the internal variables required to account for history-dependent behaviors since the RNN is self-equipped with hidden variables that have the ability of tracking loading history. On the other hand, in order to achieve accuracy under multi-dimensional non-proportional loading conditions, training of the RNN is achieved using sequential data. In particular the sequential training data are collected from finite element simulations on an elasto-plastic composite RVE subjected to random loading paths. The random loading paths are generated in a way similar to a random walking in stochastic process and allow generating data for a wide range of strain-stress states and state evolution. The accuracy and efficiency of the RNN-based surrogate model is tested on the structural analysis of an open-hole sample subjected to several loading/unloading cycles. It is shown that a similar accuracy as with a FE2 multi-scale simulation can be reached with the RNN-based surrogate model as long as the local strain state remains in the training range, while the computational time is reduced by four orders of magnitude.