Fracture mechanics analysis of two-dimensional cracked thin structures (from micro- to nano-scales) by an efficient boundary element analysis

Abstract In this paper, the boundary element method (BEM) based on the elasticity theory is developed for fracture analysis of cracked thin structures with the relative thickness-to-length ratio in the micro- or nano-scales. A special crack-tip element technique is employed for the direct and accurate calculation of stress intensity factors (SIFs). The nearly singular integrals, which are crucial in applying the BEM for thin-structural problems, are calculated accurately by using a nonlinear coordinate transformation method. The present BEM procedure requires no remeshing procedure regardless of the thickness of thin structure. Promising SIFs results with only a small number of boundary elements can be achieved with the relative thickness of the thin film is as small as 10−9, which is sufficient for modeling most of the thin bodies as used in, for example, smart materials and micro/nano-electro-mechanical systems.