Analysis of generalized T-stress for cracks in 3D linear piezoelectric media under various crack-face conditions by BEM

Abstract

This thesis presents an efficient and accurate numerical procedure for the determination of the generalized T-stress components of cracks in a three-dimensional, linear piezoelectric, infinite medium under various crack-face conditions. The key formulation is established in terms of dual weak-form boundary integral equations involving only the crack-face data and weakly singular kernels. This pair of integral equations is then integrated with one of the four crack-face conditions including impermeable, permeable, semi-permeable and energetically consistent conditions to form the complete boundary value problem for a piezoelectric cracked medium. The boundary integral equation for the jump in the crack-face generalized traction coupled with the crack-face condition is solved first for the jump in the crack-face generalized displacement. In the solution procedure, a weakly singular symmetric Galerkin boundary element method and the special near-front approximation are adopted in the discretization whereas a system of nonlinear algebraic equations arising from the semi-permeable and energetically consistent crack-face conditions is solved by standard Newton-Raphson algorithm. Once the jump in the crack-face generalized displacement is completely determined, the sum of the crack-face generalized displacement is then obtained by solving the remaining integral equation via a standard Galerkin technique. This solved crack-face data is then employed to directly extract the generalized T-stress components along the crack front. Results from numerical experiments of various scenarios indicate that the proposed technique yields highly accurate numerical solutions and is computationally robust. In addition, the predicted generalized T-stresses are significantly influenced by the crack-face condition adopted in the modeling.