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.

中文翻译：

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声子的 Vlasov 方程及其宏观后果

摘要

对于立方晶体的松弛近似中的超弹性理论的一阶，获得了对调和近似的修正。Vlasov 方程是为自洽变形场中的无碰撞声子气体构建的。在平衡分布的松弛近似中考虑了声子的碰撞。结果表明，热弹性方程对于处于热力学极限的声子气体的流体力学是有效的。考虑了声子气体的动力学模型与 Cattaneo 和 Guyer-Crumhansl 方程以及 Biot 热弹性之间的关系。