Implementation of the extended finite element method for dynamic thermoelastic fracture initiation

The eXtended Finite Element Method (XFEM) is implemented to model the effect of the mechanical and thermal shocks on a body with a stationary crack. The classical thermoelasticity equations are considered. The Newmark and the Crank–Nicolson time integration schemes are used to solve the dynamical system of matrix equations obtained from the spatial discretization of the elastic and thermal parts respectively. The variation of dynamical stress intensity factors versus time are computed by the interaction integral method. A C++code is developed to do the different stages of the calculations from mesh generation to the calculation of interaction integrals. Several elastic and thermoelastic numerical examples are implemented, where the dynamical behaviour of the face and tip enrichments of XFEM are investigated and the results are discussed in detail.