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International Journal for Multiscale Computational Engineering
IF: 1.016 5-Year IF: 1.194 SJR: 0.452 SNIP: 0.68 CiteScore™: 1.18

ISSN Print: 1543-1649
ISSN Online: 1940-4352

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.2018026858
pages 377-395

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

Daniel Vallicotti
Institute of Applied Mechanics, Department of Civil and Environmental Engineering, University of Stuttgart, 70569 Stuttgart, Pfaffenwaldring 7, Germany
Ashish Sridhar
Institute of Applied Mechanics, Department of Civil and Environmental Engineering, University of Stuttgart, 70569 Stuttgart, Pfaffenwaldring 7, Germany
Marc-Andre Keip
Institute of Applied Mechanics, Department of Civil and Environmental Engineering, University of Stuttgart, 70569 Stuttgart, Pfaffenwaldring 7, Germany

ABSTRACT

This paper presents a variationally consistent approach of computational homogenization to large-deformation micro-electro-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.


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