Fracture Mechanics Analysis of Two-Dimensional Cracked Thin Structures (from Micro- to Nano-Scales) by an Efficient Boundary Element Analysis

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.