Mechanical equilibrium of a heated anharmonic solid

A new substantiation has been proposed for for the dependence of the dynamic part of the thermal energy of an anharmonic solid on its strain in terms of the perturbation theory in the anharmonicity constant. The inclusion of this dependence in the internal energy of a solid leads to the fact that the so-called “thermal” pressure force is added to internal elasticity forces. The solution of the equation of the mechanical equilibrium is the equation of state of the solid—the dependence of its macroscopic deformation on temperature and external load. In the absence of external forces, the mechanical equilibrium of the heated solid is reduced to the equilibration of internal forces, which makes it possible to determine the thermal strain of the solid, and the dependence of the strain on the external load also explains the thermoelastic effect—the variation in the solid temperature during its adiabatic mechanical loading. It is shown that the thermal and mechanical strains are summed in the first order of the perturbation theory.