A nonlocal macro-meso-scale damage model based modeling for crack propagation in ferroelectric materials

The accurate simulation of crack growth for ferroelectric materials plays a crucial role in the application of ferroelectric materials in electronic devices. In recent years, a nonlocal macro-meso-scale consistent damage (NMMD) model has been proposed for simulating the crack propagation in brittle materials, which offers the advantage of higher efficiency compared to the phase-field method. Different from the phase field method, this model does not need to solve the phase field equation at the same time. Therefore, the degree of freedom in solving can be reduced, thereby reducing the computational workload. In this paper, the authors proposed a new integration strategy for microscopic damage and devised a simple and efficient implementation of the NMMD model for the modelling of quasi-static fracture in the general purpose commercial software developer, COMSOL Multiphysics based on the finite element method (FEM) and studied the crack propagation for ferroelectric materials under the applied stress and electric fields. Different from the original NMMD model, only the tensile stress induced geometric damage is accounted for crack propagation by using the decomposition of elastic strain energy. The effects of different crack-face conditions, electrical boundary conditions and the electromechanical loading for crack growth of ferroelectric materials have been considered in our FEM simulation are discussed in this work.