A comprehensive study on the 2D boundary element method for anisotropic thermoelectroelastic solids with cracks and thin inhomogeneities

This paper develops Somigliana type boundary integral equations for 2D thermoelectroelasticity of anisotropic solids with cracks and thin inclusions. Two approaches for obtaining of these equations are proposed, which validate each other. Derived boundary integral equations contain domain integrals only if the body forces or distributed heat sources are present, which is advantageous comparing to the existing ones. Closed-form expressions are obtained for all kernels. A model of a thin pyroelectric inclusion is obtained, which can be also used for the analysis of solids with impermeable, permeable and semi-permeable cracks, and cracks with an imperfect thermal contact of their faces. The paper considers both finite and infinite solids. In the latter case it is proved, that in contrast with the anisotropic thermoelasticity, the uniform heat flux can produce nonzero stress and electric displacement in the unnotched pyroelectric medium due to the tertiary pyroelectric effect. Obtained boundary integral equations and inclusion models are introduced into the computational algorithm of the boundary element method. The numerical analysis of sample and new problems proved the validity of the developed approach, and allowed to obtain some new results.