A mode decoupling continuum shape sensitivity method for fracture analysis of functionally graded materials

In this paper new mode decoupling continuum shape sensitivity method for calculating mixed-mode stress-intensity factors for a stationary crack in two-dimensional, linear-elastic, functionally graded materials with arbitrary geometry is presented. The proposed method involves the mode decoupling of deformations, the material derivative concept taken from continuum mechanics, and direct differentiation. The discrete form of the energy release rate is simple and easy to calculate, as it only requires multiplication of displacement vectors and stiffness sensitivity matrices. By judiciously selecting the velocity field, the method only requires displacement response in a sub domain close to the crack tip, thus making the method computationally efficient. Excellent agreement is obtained between stress-intensity factors predicted by the proposed method and available reference solutions in the literature. Therefore, mode decoupling shape sensitivity analysis provides an attractive alternative to fracture analysis of cracks in homogeneous and non-homogeneous materials.