Boundary integral equations and the boundary element method for fracture mechanics analysis in 2D anisotropic thermoelasticity

This paper develops the Somigliana type boundary integral equations for fracture of anisotropic thermoelastic solids using the Stroh formalism and the theory of analytic functions. In the absence of body forces and internal heat sources, obtained integral equations contain only curvilinear integrals over the solid’s boundary and crack faces. Thus, the volume integration is eliminated and also there is no need to evaluate integrals over the contours in the mapped temperature domain as it was done before. In addition to finite solids, the case of an infinite anisotropic medium with a remote thermal load is also studied. The dual boundary element method for fracture of anisotropic thermoelastic solids is developed based on the obtained boundary integral equations. Presented numerical examples show the validity and efficiency of the obtained equations in the analysis of both finite and infinite solids with cracks.