Computational homogenization of nonlinear elastic materials using neural networks

TLDR

The study proposes a decoupled computational homogenization method for nonlinear elastic materials that employs neural networks. The method represents the effective potential as a response surface parameterized by macroscopic strains and microstructural parameters, with discrete values computed via finite element sampling and neural networks used to approximate the surface and derive macroscopic stress and tangent tensors. Numerical convergence analyses demonstrate that smooth functions can be efficiently evaluated in up to ten‑dimensional parameter spaces, enabling three‑dimensional representative volume elements and explicit dependence on microstructural parameters such as volume fraction, and the technique is applied to homogenize nonlinear elastic composites, including a two‑scale graded nonlinear structure. © 2015 John Wiley & Sons, Ltd.

Abstract

Summary In this work, a decoupled computational homogenization method for nonlinear elastic materials is proposed using neural networks. In this method, the effective potential is represented as a response surface parameterized by the macroscopic strains and some microstructural parameters. The discrete values of the effective potential are computed by finite element method through random sampling in the parameter space, and neural networks are used to approximate the surface response and to derive the macroscopic stress and tangent tensor components. We show through several numerical convergence analyses that smooth functions can be efficiently evaluated in parameter spaces with dimension up to 10, allowing to consider three‐dimensional representative volume elements and an explicit dependence of the effective behavior on microstructural parameters like volume fraction. We present several applications of this technique to the homogenization of nonlinear elastic composites, involving a two‐scale example of heterogeneous structure with graded nonlinear properties. Copyright © 2015 John Wiley & Sons, Ltd.