基于流体动力学理论的颗粒物质本构关系

利用流体动力学(hydrodynamic)方法, 普通固体的弹性理论能自然地推广到颗粒物质, 从而得到一组可用来具体计算包括应力、变形、能量、能流、热产生等所有物理量在内的完备偏微分方程. 特别地, 它们能确定具有重要工程意义、至今尚未完全建立的颗粒物质本构关系. 本文具体推导了这个本构关系的一般热力学表达式. 结果显示, 即使在自由能模型和耗散系数都比较简单的情况下, 本构关系也是非常复杂的非线性关系, 有繁多的关于应力、速度、密度等变量的空间导数项. 因此, 直接从实验数据建立严格的, 特别是非均匀情况下的本构关系将是一件非常困难的事情.

A granular constitutive relation derived from hydrodynamics

Employing the hydrodynamic approach, normal elasticity theory is generalized in a natural way to account for granular media. The result is a set of partial differential equations that can be used to calculate all relevant physical quantities, including stress, deformation, energy, energy flux and heat production. Especially, a constitutive relation appropriate for granular media and expressed in thermodynamic quantities—— something of great engineering significance and not yet fully established—— is deduced from the theory. This constitutive relation is complex and nonlinear, containing gradients of stress, velocity and density, even for the simplest possible input of a free energy expression and transport coefficients. This amply demonstrates the difficulties of arriving at an appropriate constitutive relation starting directly from experimental data.