A Micromechanical Model for Damage Evolution in Thin Piezoelectric Films

Thin-film piezoelectric materials are advantageous in microelectromechanical systems (MEMS), due to large motion generation, high available energy and low power requirements. In this kind of application, thin piezoelectric films are subject to mechanical and electric cyclic loading, during which damage can accumulate and eventually lead to fracture. In the present study, continuum damage mechanics and asymptotic theory are adopted to model damage evolution in piezoelectric thin films. Our purpose is to develop a new interface model for thin piezoelectric films accounting for micro-cracking damage of the material. The methods used are matched asymptotic expansions, to develop an interface law, and the classic thermodynamic framework of continuum damage mechanics combined with Kachanov and Sevostianov’s theory of homogenization of micro-cracked media, to characterize the damaging behavior of the interface. The main finding of the paper is a soft imperfect interface model able to simulate the elastic and piezoelectric behavior of thin piezoelectric film in the presence of micro-cracking and damage evolution. The obtained interface model is expected to be a useful tool for damage evaluation in MEMS applications. As an example, an electromechanically active stack incorporating a damaging piezoelectric layer is studied. The numerical results indicate a non-linear evolution of the macroscopic response and a damage accumulation qualitatively consistent with experimental observations.