Implementation of the numerical manifold method for thermo-mechanical fracture of planar solids

The numerical manifold method (NMM) is developed to solve thermo-mechanical fracture problems in two-dimensional setting. The temperature fields are firstly determined through steady heat conduction analysis and then imported into the mechanical simulation. The temperature and displacement discontinuities across crack faces are essentially captured due to the dual cover systems in the NMM. To account for the singularity of thermal flux and stresses at the crack tip, the associated asymptotic basis is adopted in the cover functions for thermal and mechanical computation, respectively. The stress intensity factors are calculated with the domain-independent interaction integral. The accuracy of the proposed method is tested through several numerical examples including single, double and multiple-branched cracks and the results agree well the available solutions from the literature. The superiority of the NMM in the multi-field discontinuity modeling is preliminarily verified through the present work.