Transient dynamic analysis of a cracked functionally graded material by a BIEM

A hypersingular time-domain traction boundary integral equation method (BIEM) is presented for transient dynamic crack analysis in a functionally graded material (FGM). A finite crack in an infinite and linear elastic FGM subjected to an impact antiplane crack-face loading is investigated. The spatial variation of the materials constants is described by an exponential law. To solve the hypersingular time-domain traction BIE, a numerical solution procedure is developed. The numerical solution procedure uses a convolution quadrature formula for approximating the temporal convolution and a Galerkin method for the spatial discretization of the hypersingular time-domain traction BIE. Numerical examples are presented to show the effects of the materials gradients on the dynamic stress intensity factors.