Virtual Crack Closure Integral in BEM-Analysis of Piezoelectric Crack Problems

摘要

This study deals with the computation of crack problems in two-dimensional piezoelectric solids under combined static electrical and mechanical loading. A direct collocation boundary element code is presented, which is based on a fast numerical algorithm to compuite the piezoelectric fundamental solutions. Furthermore, the substructure technique (multi-domain) is used to model dissimilar material regions and to discretize cracks in an efficient manner. Directly at the crack tips discontinuous quarter-point elements are used to represent the typical r~(-1/2)-singular behaviour of the near tip solution with high accuracy. By investigating the BEM-solution, the stress and dielectric displacement intensity factors can be obtained quite accurately and comfprtably. A new technique is developed to determine the electromechanical energy release rate. The virtual crack closure integral is adapted to the BEM formulation and the special crack tip elements. This technique is capable to deliver the energy release rate separatd into the individual modes I, II and IV with high accuracy. In order to demonstrate and to verify the method, the electromechanical Griffith crack and an interface problem are analysed.