Journal
COMPUTATIONAL MECHANICS
Volume 68, Issue 5, Pages 1111-1130Publisher
SPRINGER
DOI: 10.1007/s00466-021-02061-x
Keywords
Nonlinear multiscale simulation; Metamaterials; Constitutive modeling; Anisotropic hyperelasticity; Machine learning
Funding
- Department of Mechanical Engineering at TU Darmstadt
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A sequential nonlinear multiscale method is proposed for simulating elastic metamaterials subjected to large deformations and instabilities. The method involves inducing buckling in cubic beam lattice unit cells through stochastic perturbation, training anisotropic effective constitutive models using artificial neural networks, and conducting macroscopic nonlinear finite element simulations. The approach accurately reproduces highly nonlinear behavior of 3D metamaterials at lesser computational effort.
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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