砂土的流体动力学方程与本构模型的比较  

Hydrodynamic method versus constitutive modeling in geotechnical materials

作　　者：蒋亦民[1,2] 刘佑[3] 

机构地区：[1]中南大学物理科学与技术学院,长沙410083 [2]中南大学粉末冶金国家重点实验室,长沙410083 [3]蒂宾根大学理论物理研究所

出　　处：《岩土力学》2010年第6期1729-1738,共10页Rock and Soil Mechanics

摘　　要：目前砂土材料连续力学方程建模有两种途径,一种是源自于论证Navier-Stokes方程时所用的方法,称为流体动力学方法,主要针对普通固体、普通流体、超流、液晶、高聚物、颗粒物质等材料,它的基本做法是先给出守恒变量(如能量、动量、熵等)和对称破缺变量(如弹性应变、量子相位等)的一般运动方程,再用与具体材料有关的热力学函数和迁移系数来封闭它们;另一种方法是本构模型法,针对有塑性固体、非牛顿流体、砂土材料等材料,该做法特点是直接构建应力、应变、应力率、应变率、速度、密度、温度等变量之间的函数关系,并以此来封闭连续和牛顿方程。近年来采用这两种方法建立的砂土方程在文献上都有报道,因此,有必要对两者的特色、科学基础、适用范围,包括概念上的和具体方程等,进行比较,作为颗粒物理与土力学之间跨学科交流的一种尝试和沟通。通过比较得出,两种建模途径对表征砂土状态的完备变量集、屈服面、与塑性有关的耗散等使用了很不一样的思路和方程。We discuss the methods usually employed for continuous mechanical modeling of geotechnical materials,of which roughly speaking there are two. The first--called hydrodynamic because it was originally used for deriving the Navier-Stokes equations--is mainly adopted by physicists,who applied it to systems such as solids,superfluid,liquid crystals,polymer solutions and granular matter. To set up and close the set of differential equations,it starts from generally valid principles including thermodynamics （especially its second law,or the positivity of entropy production）,conservation laws （for mass,energy and momentum）,and the concept of spontaneously broken-symmetry （for variables such as elastic strain or quantum phase）. The second approach to continuous mechanics is constitutive modeling,usually employed by engineers for the study of systems such as plastic solids,non-Newtonian fluids,geotechnical materials. It aims to directly construct functional relations among stress,strain,their rates,velocity,density and temperature,and use these to close momentum conservation （i.e. the force balance）. Since both hydrodynamic and constitutive modeling for geotechnical materials are reported in the literature recently,it is worthwhile--as we do,concisely,in the present paper–to clarify their respective ideology and range of validity,and discuss their similarities and differences. We point out especially what the complete set of state variables in either theory is,and how the treatment of the yield surface and plastic dissipation differ.

关 键 词：本构模型 流体动力学 热力学 颗粒物理 

分 类 号：O469[理学—凝聚态物理]