X-FEM BASED CONTINUUM SHAPE SENSITIVITY METHOD FOR FRACTURE ANALYSIS OF CRACKS

摘要

This paper presents extended finite element method (X-FEM) based continuum shape sensitivity method for calculating the mixed-mode stress-intensity factors of a stationary crack in two-dimensional, linear-elastic, orthotropic materials with arbitrary geometry. The method involves the material derivative concept taken from continuum mechanics, the mutual potential energy release rate, and direct differentiation. The governing variational equation is differentiated prior to discretization. The discrete form of the mutual potential energy release rate is simple and easy to calculate, as it only requires multiplication of displacement vectors and stiffness sensitivity matrices. X-FEM based numerical examples, which comprise mode-I and mixed-mode deformations, are presented to evaluate the accuracy of the fracture parameters calculated by the proposed method. Comparisons have been made between stress-intensity factors predicted by the proposed method and available reference solutions in the literature, generated either analytically or numerically using various other fracture integrals or analyses.