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A. Humer, E. Hansy-Staudigl, M. Krommer:
"Nonlinear electro-elasticity for piezoelectric materials and structures using a multiplicative decomposition of the deformation gradient";
in: "Proc. of VIII ECCOMAS Thematic Conference on Smart Structures and Materials - SMART 2017", A. Güemes, A. Benjeddou, J. Rodellar, J. Leng (ed.); CIMNE, 2017, 12 pages.

Nonlinear modeling of the inelastic behavior of materials by a multiplicative de- composition of the deformation gradient tensor is commonly used in geometrically nonlinear problems. Among the various scope of problems, the decomposition has proven applicable in thermoelasticity, elastoplasticity, as well as for the description of residual stresses arising in growth processes of biological tissues. In the context of smart materials, electro-elastic elas- tomers, shape-memory alloys and piezoelectric materials have been considered. The present paper reviews the nonlinear field equations of electro-elasticity and provides a general represen- tation of the constitutive equations adopting the multiplicative decomposition of the deformation gradient. In extension to previous contributions, the electrostatic body forces and couples are consistently accounted for within the framework of thermodynamics. Exemplarily, the general relations are particularized for a simple choice of free energy functions.

Nonlinear electro-elasticity, constitutive modeling, multiplicative decomposition, smart materials

https://publik.tuwien.ac.at/files/publik_264997.pdf