Analysis of the embedded cell method for the numerical homogenization of metal-ceramic composite materials

TL;DR

This paper analyzes the embedding cell method for numerical homogenization of metal-ceramic composites, demonstrating convergence and consistency with analytical homogenization in various models.

Contribution

It provides a convergence proof and validation of the embedding cell method against analytical homogenization for different material models.

Findings

Convergence of the embedding cell method iteration scheme.

Coincidence of predicted and effective material properties.

Validation across linear elasticity, plasticity, and hyperelastic models.

Abstract

In this paper, we analyze the embedding cell method, an algorithm which has been developed for the numerical homogenization of metal-ceramic composite materials. We show the convergence of the iteration scheme of this algorithm and the coincidence of the material properties predicted by the limit with the effective material properties provided by the analytical homogenization theory in three situations, namely for a one dimensional linear elasticity model, a simple one dimensional plasticity model and a two dimensional model of linear hyperelastic isotropic materials with constant shear modulus and slightly varying first Lam\'e parameter.