A BDEM for transient thermoelastic crack problems in functionally graded materials under thermal shock

A boundary-domain element method for solving transient crack problems of linear coupled thermoelasticity in two-dimensional, finite, isotropic, continuously non-homogeneous and linear elastic functionally graded materials subjected to a thermal shock is developed. Fundamental solutions of linear coupled thermoelasticity in Laplace-transformed domain for isotropic, homogeneous and linear elastic solids are applied to derive a boundary-domain integral equation formulation. A collocation method is implemented for the spatial discretization. To obtain the time-dependent solutions the Stehfest’s algorithm is used. Thermal dynamic stress intensity factors are evaluated by using the extrapolation technique. Numerical examples for an exponential gradation of the material parameters are presented and discussed to show the effects of the material gradation and the coupling parameter on the thermal dynamic stress intensity factors.