Postbuckling investigations of piezoelectric microdevices considering damage effects

Piezoelectric material has been emerging as a popular building block in MEMS devices owing to its unique mechanical and electrical material properties. However, the reliability of MEMS devices under buckling deformation environments remains elusive and needs to be further explored. Based on the Talreja's tensor valued internal state damage variables as well as the Helmhotlz free energy of piezoelectric material, a constitutive model of piezoelectric materials with damage is presented. The Kachanvo damage evolution law under in-plane compressive loads is employed. The model is applied to the specific case of the postbuckling analysis of the piezoelectric plate with damage. Then, adopting von Karman's plate theory, the nonlinear governing equations of the piezoelectric plates with initial geometric deflection including damage effects under in-plane compressive loads are established. By using the finite difference method and the Newmark scheme, the damage evolution for damage accumulation is developed and the finite difference procedure for postbuckling equilibrium path is simultaneously employed. Numerical results show the postbuckling behaviors of initial flat and deflected piezoelectric plates with damage or no damage under different sets of electrical loading conditions. The effects of applied voltage, aspect ratio of plate, thick-span ratio of plate, damage as well as initial geometric deflections on the postbuckling behaviors of the piezoelectric plate are discussed.