Analysis of the embedded cell method for the numerical homogenization of metal-ceramic composite materials
For researchers in computational materials science, this provides theoretical justification for an existing numerical method, but the analysis is limited to simplified models.
The paper proves convergence of the embedded cell method for numerical homogenization of metal-ceramic composites and shows that its limit matches analytical homogenization theory in 1D linear elasticity, 1D plasticity, and 2D linear hyperelasticity with varying Lamé parameter.
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 Lamé parameter.