VARIATIONALLY CONSISTENT COMPUTATIONAL HOMOGENIZATION OF MICRO-ELECTRO-MECHANICS AT FINITE DEFORMATIONS

摘要

This paper presents a variationally consistent approach of computational homogenization to large-deformation microelectro-mechanics. It links a phase field model for micro-structure evolution in ferroelectrics to an electro-mechanical macro-continuum by extending existing small-strain approaches to finite deformations. The variationally consistent two-scale solution scheme is based on a rate-type variational principle that incorporates the polarization as microscopic order parameter. It enables combined electro-mechanical loading conditions of representative volume elements by means of a generalized macroscopic driving routine. The proposed scheme allows for the computation of effective quantities such as stresses and electric displacements as well as the associated moduli. These quantities directly depend on the domain configurations of the ferroelectric phases at the micro-level. We demonstrate the capabilities of the proposed formulation by a set of academic numerical examples that showcase the considered electro-mechanical coupling phenomena at micro- and macro-scale.