Adaptive finite element computation of dielectric and mechanical intensity factors in piezoelectrics with impermeable cracks

Abstract

SUMMARYThe paper deals with the application of an adaptive, hierarchic-iterative finite element technique to solve two-dimensional electromechanical boundary value problems with impermeable cracks in piezoelectric plates. In order to compute the dielectric and mechanical intensity factors, the interaction integral technique is used. The iterative finite element solver takes advantage of a sequence of solutions on hierarchic discretizations. Based on an a posteriori error estimation, the finite element mesh is locally refined or coarsened in each step. Two crack configurations are investigated in an infinite piezoelectric plate: A finite straight crack and a finite kinked crack. Fast convergence of the numerical intensity factors to the corresponding analytical solution is exemplarily proved during successive adaptive steps for the first configuration. Similar tendency can be observed for the second configuration. Furthermore, the computed intensity factors for the kinks are found to coincide well with the corresponding analytical values. In order to simulate the kinks spreading from a straight crack, the finite element mesh is modified automatically with a specially developed algorithm. This forms the basis for a fully adaptive simulation of crack propagation.

Extended isogeometric dynamic and static fracture analysis for cracks in piezoelectric materials using NURBS

“…Previous works also provided many analytical solutions as well as proposed the theoretical fundamentals of fracture problems for piezoelectric materials in terms of linear elastic fracture mechanics [10,11] The FEM has applied to model fracture problems in piezoelectric materials. After the first couple of works by Kumar and Singh [12,13], a large number of subsequent contributions in this direction have been made, e.g., see [2,[14][15][16][17][18][19]. Special singular crack-tip elements, crack closure integrals, electro-mechanical J-integral, and so on have been developed for evaluating fracture parameters (e.g., intensity factors, energy release rate) for piezoelectric materials.…”