Finite element modeling of electro-mechanically coupled analysis for ferroelectric ceramic materials with defects

In light of the equations of static mechanical and electrical equilibrium of ferroelectric materials, the functional is presented by using the principle of virtual work in this paper. Formulation of the electro-mechanically coupled finite element analysis for ferroelectric materials with defects has been described in details. The effect of depolarization in ferroelectrics has been taken into account in the formulation. In addition, various electric boundary conditions on the crack surfaces in ferroelectric ceramics are implemented in the finite element procedure developed. Thus, the current finite element method (FEM) has been extended to account for the impermeable, permeable and conducting cracks, by considering that the crack gap is filled with homogenous dielectric media. As an example, the crack propagation of a double edge notched specimen of a PZT-5H ferroelectric ceramic with exact electric boundary conditions on the crack surfaces is analyzed.