基于流体动力学理论的颗粒物质本构关系
摘要
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.