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FFT‐based Homogenization in nonlinear Electroelasticity
Author(s) -
Göküzüm Felix Selim,
Nguyen Lu Trong Khiem,
Keip MarcAndré
Publication year - 2018
Publication title -
pamm
Language(s) - English
Resource type - Journals
ISSN - 1617-7061
DOI - 10.1002/pamm.201800128
Subject(s) - homogenization (climate) , preconditioner , solver , fast fourier transform , nonlinear system , rate of convergence , mathematics , fourier transform , tangent , mathematical analysis , iterative method , materials science , computer science , mathematical optimization , physics , algorithm , geometry , channel (broadcasting) , computer network , quantum mechanics , biology , biodiversity , ecology
Electroactive polymers (EAPs) are a group of materials that is able to respond with large strains to applied electric fields, making them candidates for applications such as artificial muscles or smart fins. The present contribution addresses the computational homogenization of electroactive materials based on fast‐Fourier‐transforms. The focus lies on the formulation of a coupled Lippmann‐Schwinger equation with respect to the deformation gradient as well as the electric displacement, where the reference medium introduced in the Lippmann‐Schwinger equation is also fully coupled. As the reference medium is acting as a preconditioner on the system, this has an impact on the convergence rate and stability of the iterative solver. We provide an algorithmically consistent coupled tangent operator as alternative to finite‐difference based approaches.