Hamed [24] presented a nonlinear theoretical model for their bending and creep buckling analysis. The model accounted for the viscoelasticity of the materials using differential-type constitutive relations that were based on the linear Boltzmann’s principle of superposition. Xu et al. [25] presented a high performance and simple structure bi-stable piezoelectric energy harvester based on simply supported piezoelectric buckled beam. Cottone et al. [26] investigated an approach for piezoelectric beams by exerting an increasing axial compression and demonstrated that the numerical model and experimental results were in good qualitative agreement. A constitutive model of fully coupled electro-magneto-thermo-elastic multiphase composites has been proposed by Aboudi [27].
In his works, the linear displacement, electric potential and magnetic potential are adopted, which can’t predict the micro fields precisely. Bansal and Pindera [28] proposed a unified macro-and micro-mechanics failure model with method of cells as finite-volume direct averaging micromechanics (FVDAM). Based on the FVDAM theory, Sun et al. [29] built a unified macro- and micro-mechanics constitutive model of fully coupled fields in composite materials by high-order displacement, electric potential and magnetic potential.In the present study, a new constitutive model for piezoelectric materials using the Talreja’s tensor valued internal state damage variables and the Helmhotlz free energy of piezoelectric material is presented. This model is then applied to a specific case of postbuckling analysis of piezoelectric plates under in-plane compressive loads.
By adopting von Karman’s plate theory and using the finite difference and the Newmark scheme, the damage evolution for damage accumulation is developed and the finite difference procedure for postbuckling equilibrium path is simultaneously employed. In the numerical examples, the effects of variation in the load parameters, damage influences and geometric parameters of the plate on postbuckling equilibrium paths are discussed.2.?Basic Equations2.1. Constitutive Equations for Damaged Piezoelectric MaterialsConsider a representative volume element of a piezoelectric solid with a multitude of damage entities in the fo
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