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

Til Gärtner,Oliver Weeger,Mauricio Fernández

doi:10.1007/s00466-021-02061-x

Abstract

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.

Highlights

Recent progress in Additive Manufacturing (AM) and microfabrication technologies has opened up a whole new set of possibilities for the realization of metamaterials, i.e., artificial microstructures that exhibit properties and behaviors extending beyond the capabilities of ordinary materials [1]
The mechanical modeling of such flexible beam lattices is challenging, since their microstructure and soft material constituents allow for geometrically large elastic deformations that are accompanied by instabilities due to strut buckling [7,18], resulting in a highly nonlinear and anisotropic effective behavior
A sequential nonlinear multiscale method for the simulation of elastic beam lattices was developed in this work, showing that metamaterials subject to large deformations and instabilities can be efficiently and accurately described using highly flexible, data-driven effective constitutive models formulated upon artificial neural networks

Summary

Introduction

Recent progress in Additive Manufacturing (AM) and microfabrication technologies has opened up a whole new set of possibilities for the realization of metamaterials, i.e., artificial microstructures that exhibit properties and behaviors extending beyond the capabilities of ordinary materials [1]. Multiscale simulation approaches are generally preferred for microstructured objects and metamaterials, which have already been widely applied to lattice structures in the linear, infinitesimal strain regime, for multiscale design and topology optimization [21,22,23,24]. Such approaches require that the microstructure is periodic and sufficiently small compared to the macroscale, i.e., that scales are separated. The effective behavior for the microstructure can be homogenized from a representative unit cell (RUC) to relate the stress-strain response from microscale to macroscale, where the structure can be regarded as a continuum [25]

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