Generalized Solution of Equations of Dynamics of Thermoelastic Medium with Crack

Abstract

The dynamics of an isotropic thermoelastic medium during the formation of cracks with an arbitrary surface geometry and non-opening edges is considered. The shock thermoelastic waves arise in the medium during such a process. The energy conservation law for a thermoelastic medium is considered considering shock waves. For shock thermoelastic waves, using the method of generalized functions, conditions are obtained for jumps in stresses, velocities, heat fluxes and energy density on their fronts. The crack model determines the relationship between jumps in stresses and velocities of relative displacement of the crack edges. The problem is posed and solved in the space of generalized vector functions. The solution is presented as a tensor-functional convolution of the Green’s tensor of the equations of coupled thermoelasticity with a singular mass forces containing simple and double layers whose densities are determined by the jump in velocities, stresses, temperatures and heat fluxes on the crack edges. The latter determine the crack model and are assumed to be known.