Upper and lower bounds analysis of electric induction intensity factors for multiple piezoelectric cracks by the BEM

Abstract

For piezoelectric cracks, the correct magnitudes of the electric induction intensity factors (EIFs) are obtained by the semi-permeable boundary condition (BC) the solution procedure of which is a non-linear iterative process that are not well established so far. We propose to use the impermeable and permeable BCs, although not correct, to obtain the upper and lower bounds of the EIFs using much simpler linear solution procedure by the boundary element method (BEM). We develop a numerical Green's function approach based on the whole crack singular element (WCSE) for the general piezoelectric solids in two-dimensions. It is used for the mixed mode boundary element analysis of multiple straight cracks for impermeable and permeable BCs. The crack opening displacement (COD) of a straight crack is represented by the continuous distribution of dislocation dipoles, with the built-in r COD behavior, which is integrated analytically to give the r COD and the 1 / r crack tip stress singularity. The proposed numerical Green's function approach does not require the post-processing for the accurate determination of the stress intensity factors (SIFs).