Numerical simulation of thermo-elastic fracture problems using element free Galerkin method

Abstract

In the present work, element free Galerkin method (EFGM) has been extended to solve thermo-elastic fracture problems in homogeneous and inhomogeneous materials (bi-materials). A thermo-elastic fracture problem is decoupled into two separate problems. At first, the temperature distribution is obtained by solving the heat transfer problem. The temperature field is then employed as input for the mechanical problem to determine the displacement and stress fields. The disturbances due to the presence of crack results in a non-smooth temperature distribution, and induces a singularity in the heat flux at the crack tip. Thermal as well as mechanical problems are enriched intrinsically in order to represent the discontinuous temperature, heat flux, displacement and traction across the crack surfaces. Both isothermal and adiabatic conditions are considered at the crack surfaces. Jump function technique has been employed to model a bi-material interface, and intrinsic enrichment has been used to model a crack at the bi-material interface. The conservative M-integral technique has been modified in order to extract the mixed mode stress intensity factor for thermo-elastic fracture problems. The present analysis shows that the results obtained by EFGM are in good agreement with those available in the literature.