MATHEMATICAL MODEL OF LOCALLY NONEQUILIBRIUM COUPLED DYNAMIC THERMOELASTICITY

When setting the classical problem of coupled dynamic thermoelasticity, as a rule, a quasi-stationary or locally equilibrium model is used, in which temperature changes throughout the entire volume of the body are small, the deformation of a physically small volume linearly depends on displacement. The connection of heat transfer with displacement is carried out by adding a term proportional to the rate of change of deformation of the body to the equation of thermal conductivity, and a term proportional to the temperature gradient to the wave equation. One of the main disadvantages of this model is the infinite velocity of temperature propagation and deformation and the inability to describe fast processes with large amplitudes of temperature change and displacement. Using modified formulas of empirical Fourier and Hooke laws, which take into account the rates of change of moving forces –causes (temperature gradients and displacements) and their consequences (heat flux and stress), a mathematical model of coupled dynamic thermoelasticity under heat shock conditions is obtained. The model includes an interconnected system of nonlocal equations of thermal conductivity and dynamic thermoelasticity, which takes into account the dual-phase delay in thermal and thermoelastic problems, as well as the resistance of the medium to the process of changing its shape as a result of temperature deformation. The analysis of the obtained analytical solution of the model showed that deformation and temperature propagate in a medium with similar velocities.