Two-scale computational homogenization of electro-elasticity at finite strains

This contribution addresses a two-scale computational homogenization framework for the simulation of electro-active solids at finite strains. A generalized form of the Hill-Mandel condition is employed for the derivation of energetically consistent transition conditions between the scales. The continuum mechanical formulation is implemented into a two-scale finite element environment, in which we attach a microscopic representative volume element at each integration point of the macroscopic domain. In order to allow for an efficient solution of the macroscopic boundary value problem an algorithmically consistent tangent of the macroscopic problem is derived. The method will be applied to the analysis of dielectric polymer-ceramic composites, where we determine the effective actuation of composites with different microstructures. Furthermore, we show the applicability of the proposed method to the computation of two-scale electro-mechanically coupled boundary value problems in consideration of large deformations.