Weakly singular boundary integral equation method for analysis of generalized T-stresses of cracks in 3D coupled-field media

Abstract

This thesis presents the development of a weakly singular boundary integral equation method for the analysis of the generalized T-stress of isolated cracks embedded in a coupled-field whole space. A pair of weak-form integral equations, one for crack-face generalized traction and the other for the gradient of the crack-face generalized displacement, is established in a general framework allowing various types of materials including elastic, piezoelectric, piezomagnetic and piezoelectromagnetic solids, general crack geometry and loading conditions to be handled in a unified fashion. In addition, the final governing integral equations contain only weakly singular kernels and this, as a result, renders the integral interpretation in terms of Riemann sum and the use of continuous basis functions in the approximation possible. Both symmetric Galerkin boundary element method and the Galerkin technique are employed to solve the pair of weak-form integral equations. Special near-front approximation is also employed to enhance the quality of solution near the crack front with the use of relatively coarse meshes. Explicit formula in terms of the gradient of the sum of the crack-face generalized displacement along the crack front is proposed to extract the generalized T-stress. Extensive results are reported not only to validate the present technique but also to demonstrate its capability and computational robustness