Assessment of connectivity in the thermal conductivity equation of the dynamic theory of thermal elasticity for one class of brittle materials

The heat conduction equation of the coupled dynamic theory of thermoelasticity is considered. An assessment is made of the connectivity in the heat conduction equation for a space with a constant initial temperature, containing a flat semi-infinite crack moving at a constant speed, on the sides of which a constant temperature is instantly established, less than the initial one (thermal shock). The movement of a crack and thermal shock on its shores determine dynamic effects that must be taken into account to assess connectivity in the thermal conductivity equation. It is shown that, under real conditions of thermal impact on massive bodies with cracks, dynamic effects and cohesion for materials that satisfy certain conditions imposed on their thermomechanical constants can be neglected, which makes it possible to significantly simplify the solution of problems of thermoelasticity for such bodies.