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A variational, finite‐deformation constitutive model for piezoelectric materials
Author(s) -
Mota Alejandro,
Zimmerman Jonathan A.
Publication year - 2011
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.2993
Subject(s) - piezoelectricity , deformation (meteorology) , constitutive equation , electric potential , tangent , finite strain theory , finite element method , displacement (psychology) , electric displacement field , mathematical analysis , strain energy , classical mechanics , mathematics , physics , geometry , structural engineering , engineering , acoustics , quantum mechanics , meteorology , psychotherapist , psychology , voltage
We present a constitutive model for piezoelectric materials. The model is fully variational and supports finite kinematics. The postulated free energy depends on the deformation mapping and an electric vector potential, from which the strain and the electric displacement are derived, respectively. The divergence‐free condition of the electric vector potential is enforced by means of a penalty method, which leads to a positive definite tangent for the system of equations that represent the problem. The performance of the formulation is demonstrated by several examples. Published in 2010 by John Wiley & Sons, Ltd.