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A. Humer, M. Krommer:
"Modeling of piezoelectric materials by means of a multiplicative decomposition of the deformation gradient";
Mechanics of Advanced Materials and Structures, 22(1-2) (2015), S. 125 - 135.

The present article investigates a novel approach for the constitutive modeling of piezoelectric continua subjected to large deformation and strong electric fields, which is based on a multiplicative decomposition of the deformation gradient tensor, a concept frequently used in the description of inelastic processes. By splitting the total deformation into an inelastic and a purely elastic part, the notion of a stress-free intermediate configuration is introduced, which evolves from the referential undeformed state if an electric field is present. Considering large deformations, the field equations of electromechanics need to be written in a geometrically exact form, which requires the introduction of suitable electric field quantities that fit into the Lagrangian framework adopted in the proposed formulation. To give an example of constitutive equations, the behavior of piezoelectric materials according to Voigt´s linear theory is generalized to the nonlinear case. For this purpose, the piezoelectric part of the deformation gradient is identified by comparing the corresponding nonlinear strain measures with the electrically induced strains in the linear theory of piezoelectricity. The present article discusses the implications and the quantitative influence of the choice of different strain tensors on the material response within the discussed approach.

continuum mechanics, constitutive modeling, multiplicative decomposition, piezoelectric materials, nonlinear strains

http://dx.doi.org/10.1080/15376494.2014.907948