Nonlinear dynamic response of piezoelectric elasto-plastic laminated plates with damage

Based on the elasto-plastic mechanics and continuum damage theory, a yield criterion that is related to the spherical stress tensor is proposed to describe the mixed hardening of damaged orthotropic materials, and the dimensionless form of which is isomorphic with the Mises criterion for isotropic materials. Then, the incremental elasto-plastic damage constitutive equations and damage evolution equations of orthotropic materials are established. By using the classical nonlinear plate theory, the incremental nonlinear dynamic governing equations of the piezoelectric elasto-plastic laminated plates with damage are obtained, and the equations are solved by finite difference method and iteration method. In the numerical examples, the effect of damage evolution, piezoelectric effect and external loads on the nonlinear dynamic response of elasto-plastic laminated plates are discussed detailed. The numerical results show that the mechanical properties of the structures change remarkably when considering the damage, damage evolution and piezoelectric effects.