Continuum representation of nonlinear three-dimensional periodic truss networks by on-the-fly homogenization

Glaesener, Raphaël N.; Träff, Erik; Telgen, Bastian; Canonica, Renato M.; Kochmann, Dennis M.

doi:10.1016/j.ijsolstr.2020.08.013

Cited by 27 publications

(13 citation statements)

References 36 publications

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“…The present work considers only finite material symmetry groups and denotes the number of elements in G as #(G). The material symmetry conditions for the effective potential (20) imply the following conditions on the effective first Piola-Kirchhoff stress tensor:…”

Section: Basic Materials Theory Considerationsmentioning

confidence: 99%

“…Full-scale simulation using 3D continuum finite elements (FE) is generally not feasible and also (geometrically) nonlinear 3D beam element discretizations can become computationally expensive and only feasible for lattices with a moderate amount of cells [19]. Furthermore, to resolve instabilities and ensure convergence of iterative solution schemes, nonlinear post-buckling analysis methods, such as buckling-mode perturbations [18,20], are required, which incur further computational effort and complication.…”

Section: Introductionmentioning

confidence: 99%

“…In the context of nonlinear problems, the micro-tomacro transition can either be performed concurrently, using FE 2 methods, or sequentially, using homogenized effective constitutive models [26,27]. The concurrent approach has already been successfully applied to beam lattice structures in [20,28], even including higher-gradient and curvature effects. However, it is computationally expensive, since solving a macroscale problem requires the solution of many microscale problems-one for each FE quadrature point in each iteration.…”

Section: Introductionmentioning

confidence: 99%

“…However, it is computationally expensive, since solving a macroscale problem requires the solution of many microscale problems-one for each FE quadrature point in each iteration. Furthermore, in [20] only relatively small compressive strain ranges were investigated for bucklingdominated 3D lattices (−0.6% for a BCC structure and −5% for an Octet structure), which indicates that the concurrent multiscale approach also suffers from stability issues. For sequential nonlinear multiscale simulation, the main challenge is to formulate and identify an effective constitutive model, which-in the case of elastic beam lattices-should be hyperelastic for finite elastic deformations, reflect the anisotropy/material symmetry of the microstructure, and closely represent the actual microstructural behavior, which is highly nonlinear due to differences in stretch, bending, or buckling-dominated deformations.…”

Section: Introductionmentioning

confidence: 99%

“…[52,53]. While usually eigenforms of the structure are prescribed as perturbations, see [18,20,[53][54][55], here a purely stochastic approach is pursued. As we will demonstrate, this not only reduces the manual effort of bucking eigenvalue analysis, but also significantly reduces parasitic stresses in the homogenized responses, cf.…”

Section: Introductionmentioning

confidence: 99%

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Nonlinear multiscale simulation of elastic beam lattices with anisotropic homogenized constitutive models based on artificial neural networks

2021

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A sequential nonlinear multiscale method for the simulation of elastic metamaterials subject to large deformations and instabilities is proposed. For the finite strain homogenization of cubic beam lattice unit cells, a stochastic perturbation approach is applied to induce buckling. Then, three variants of anisotropic effective constitutive models built upon artificial neural networks are trained on the homogenization data and investigated: one is hyperelastic and fulfills the material symmetry conditions by construction, while the other two are hyperelastic and elastic, respectively, and approximate the material symmetry through data augmentation based on strain energy densities and stresses. Finally, macroscopic nonlinear finite element simulations are conducted and compared to fully resolved simulations of a lattice structure. The good agreement between both approaches in tension and compression scenarios shows that the sequential multiscale approach based on anisotropic constitutive models can accurately reproduce the highly nonlinear behavior of buckling-driven 3D metamaterials at lesser computational effort.

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Section: Basic Materials Theory Considerationsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Nonlinear multiscale simulation of elastic beam lattices with anisotropic homogenized constitutive models based on artificial neural networks

2021

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Material modeling for parametric, anisotropic finite strain hyperelasticity based on machine learning with application in optimization of metamaterials

Fernández

Fritzen

Weeger

2021

Numerical Meth Engineering

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Mechanical metamaterials such as open-and closed-cell lattice structures, foams, composites, and so forth can often be parametrized in terms of their microstructural properties, for example, relative densities, aspect ratios, material, shape, or topological parameters. To model the effective constitutive behavior and facilitate efficient multiscale simulation, design, and optimization of such parametric metamaterials in the finite deformation regime, a machine learning-based constitutive model is presented in this work. The approach is demonstrated in application to elastic beam lattices with cubic anisotropy, which exhibit highly nonlinear effective behaviors due to microstructural instabilities and topology variations. Based on microstructure simulations, the relevant material and topology parameters of selected cubic lattice cells are determined and training data with homogenized stress-deformation responses is generated for varying parameters. Then, a parametric, hyperelastic, anisotropic constitutive model is formulated as an artificial neural network, extending a recent work of the author extending a recent work of the author, Comput Mech., 2021;67(2):653-677. The machine learning model is calibrated with the simulation data of the parametric unit cell. The authors offer public access to the simulation data through the GitHub repository https://github.com/CPShub/ sim-data. For the calibration of the model, a dedicated sample weighting strategy is developed to equally consider compliant and stiff cells and deformation scenarios in the objective function. It is demonstrated that this machine learning model is able to represent and predict the effective constitutive behavior of parametric lattices well across several orders of magnitude. Furthermore, the usability of the approach is showcased by two examples for material and topology optimization of the parametric lattice cell.

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LatticeGraphNet: a two-scale graph neural operator for simulating lattice structures

Jain,

Haghighat,

Nelaturi

2024

Engineering with Computers

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Continuum representation of nonlinear three-dimensional periodic truss networks by on-the-fly homogenization

Cited by 27 publications

References 36 publications

Nonlinear multiscale simulation of elastic beam lattices with anisotropic homogenized constitutive models based on artificial neural networks

Nonlinear multiscale simulation of elastic beam lattices with anisotropic homogenized constitutive models based on artificial neural networks

Material modeling for parametric, anisotropic finite strain hyperelasticity based on machine learning with application in optimization of metamaterials

LatticeGraphNet: a two-scale graph neural operator for simulating lattice structures

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