离散与连续热力学
Discrete and Continuum Thermomechanics
摘要：
在本章中，我们讨论了一种从离散到连续描述固体热机械行为的过渡方法。对一维晶体、准一维晶体（具有纵向和横向运动的链）、二维和三维简单晶格的晶体等几种非谐系统进行了跃迁。宏观平衡方程是由质点运动方程导出的。宏观参数，如应力、热通量、变形、热能等，通过离散系统的参数表示。导出了与热压、热能和比容有关的封闭状态方程。讨论了用谐波近似描述热传导的方法。本文研究一维简谐晶体中的非定常弹道热传导。严格推导了该系统的传热方程。
英文摘要：
In the present chapter, we discuss an approach for transition from discrete to continuum description of thermomechanical behavior of solids. The transition is carried out for several anharmonic systems: one-dimensional crystal, quasi-one-dimensional crystal (a chain possessing longitudinal and transversal motions), two- and tree-dimensional crystals with simple lattice. Macroscopic balance equations are derived from equations of motion for particles. Macroscopic parameters, such as stress, heat flux, deformation, thermal energy, etc., are represented via parameters of the discrete system. Closed form equations of state relating thermal pressure, thermal energy and specific volume are derived. Description of the heat transfer in harmonic approximation is discussed. Unsteady ballistic heat transfer in a harmonic one-dimensional crystal is considered. The heat transfer equation for this system is rigorously derived.
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