Abstract
Corrections to the harmonic approximation are obtained for the first order of the theory of hyperelasticity in the relaxation approximation for a cubic crystal. The Vlasov equation is constructed for a collisionless gas of phonons in a self-consistent deformation field. Collisions of phonons are considered in the relaxation approximation to the equilibrium distribution. It is shown that the thermoelasticity equations are valid for the hydrodynamics of a phonon gas in the thermodynamic limit. The relationship between the kinetic model of a phonon gas and the equations of Cattaneo and Guyer-Crumhansl, as well as Biot’s thermoelasticity, is considered.
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This study was supported by the Russian Foundation for Basic Research, project no. 20-01-00419.
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Volkov, Y.A., Dmitriev, A.S. & Markov, M.B. Vlasov Equation for Phonons and its Macroscopic Consequences. Math Models Comput Simul 13, 552–560 (2021). https://doi.org/10.1134/S2070048221040220
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DOI: https://doi.org/10.1134/S2070048221040220