Inverse analysis for heterogeneous materials and its application to viscoelastic curing polymers

Abstract

This contribution aims at achieving two important goals: First, it outlines a numerical inverse homogenization strategy able to recover material parameters of the microstructure by using results of macroscopic tests. Second, it considers parameter identification for viscoelastic heterogeneous materials, which is a step providing the basis for the further extension toward the general treatment of dissipative processes. The approach proposed couples the Levenberg---Marquardt method with the multiscale finite element method. In this combination, the former is a gradient-based optimization strategy used to minimize a merit function while the latter is a numerical homogenization technique needed to solve the direct problem. The specific example studied in the paper deals with the investigation of a composite consisting of a viscoelastic curing polymer and a nonlinear elastic material. It proposes a three-step procedure for the evaluation of its material parameters and discusses the accuracy and the uniqueness of the solution.