Energy balance in deformation mechanics of solids at low temperatures

The model of a solid in the form of an ensemble of independent anharmonic oscillators arranged in a uniform stress field has been considered to analyze the energy balance during adiabatic mechanical loading of a solid at low temperatures. Oscillator elongation is determined as the average over the ensemble, and a part of its energy is matched to this quantity. This part has the physical meaning of the mechanical energy of sample deformation and becomes a part of the energy balance upon deformation. After averaging, the uniform force field is replaced by the resultant force associated with the average deformation. Another component of the balance at low temperatures is the energy of zero-point vibrations of oscillators. Thus, upon mechanical deformation of a solid, the energy exchange occurs between two scale levels: the atomic vibration energy at a microlevel and the macroscopic deformation energy of the sample as a whole.