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

• Published in: Computational mechanics Vol. 68; no. 5; pp. 1111 - 1130
• Main Authors: Gärtner, Til, Fernández, Mauricio, Weeger, Oliver
• Format: Journal Article
• Language: English
• Published: Berlin/Heidelberg Springer Berlin Heidelberg 01.11.2021; Springer; Springer Nature B.V
• Subjects: Anisotropy; Artificial neural networks; Buckling; Classical and Continuum Physics; Computational Science and Engineering; Computer simulation; Constitutive models; Cubic lattice; Elastic anisotropy; Elastic beams; Elastic deformation; Engineering; Homogenization; Mathematical models; Metamaterials; Multiscale analysis; Neural networks; Original Paper; Perturbation; Symmetry; Theoretical and Applied Mechanics; Nonlinear multiscale simulation; Metamaterials; Constitutive modeling; Anisotropic hyperelasticity; Machine learning
• ISSN: 0178-7675; 1432-0924
• DOI: 10.1007/s00466-021-02061-x

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.