Configurational forces in a multiscale approach to piezoelectric materials

Due to the growing interest in determining the macroscopic material response of inhomogeneous materials, computational methods are becoming increasingly concerned with the application of homogenization techniques. In this work, a two-scale classical homogenization of an electro-mechanically coupled material using a FE2-approach is discussed. We explicitly formulated the homogenized coefficients of the elastic, piezoelectric and dielectric tensors for small strain as well as the homogenized remanent strain and remanent polarization. In the homogenization different representative volume elements (RVEs), which capture the micro-structure of the inhomogeneous material, are used to represent the macroscopic material response. Two different schemes are considered. In the first case, domain wall movement is not allowed, but in the second case the movement of the domain walls is taken into account using thermodynamic considerations. Later this technique is used to determine the macroscopic and microscopic configurational forces on defects [2]. These defect situations include the driving force on a crack tip. The effect of the applied electric field on configurational forces at the crack tip is investigated.