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Mathematical homogenization theory for electroactive continuum
Author(s) -
Kuznetsov Sergey,
Fish Jacob
Publication year - 2012
Publication title -
international journal for numerical methods in engineering
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.421
H-Index - 168
eISSN - 1097-0207
pISSN - 0029-5981
DOI - 10.1002/nme.4311
Subject(s) - homogenization (climate) , nonlinear system , constitutive equation , finite element method , representative elementary volume , continuum hypothesis , mathematics , classical mechanics , mathematical analysis , materials science , mechanics , physics , thermodynamics , biodiversity , ecology , quantum mechanics , biology
SUMMARY Two‐scale continuum equations are derived for heterogeneous continua with full nonlinear electromechanical coupling using nonlinear mathematical homogenization theory. The resulting coarse‐scale electromechanical continuum equations are free of coarse‐scale constitutive equations. The unit cell (or representative volume element) is subjected to the overall mechanical and electric field extracted from the solution of the coarse‐scale problem and is solved for arbitrary constitutive equations of fine‐scale constituents. The proposed method can be applied to analyze the behavior of electroactive materials with heterogeneous fine‐scale structure and can pave the way forward for designing advanced electroactive materials and devices. Copyright © 2012 John Wiley & Sons, Ltd.