基于内变量热力学的黏弹性本构方程及其基本性质研究  

A viscoelastic model and its fundamental properties based on thermodynamics with internal state variable

作　　者：张泷[1] 刘耀儒[1] 薛利军[2] 杨强[1] 

机构地区：[1]清华大学水沙科学与水利水电工程国家重点实验室,北京100084 [2]中国水电顾问集团,成都勘测设计研究院,成都610072

出　　处：《中国科学：物理学、力学、天文学》2015年第1期73-80,共8页Scientia Sinica Physica,Mechanica & Astronomica

基　　金：水沙科学与水利水电工程国家重点实验室科研项目(编号:2013-KY-2);国家自然科学基金项目(批准号:51279086,11172150)资助

摘　　要：黏弹性变形在沥青混凝土、聚合物等材料中广泛存在,也是岩石材料时效变形的重要组成部分.基于Rice不可逆内变量热力学框架,讨论材料黏弹性变形行为.引入一组内变量表征材料系统内部结构的变化,通过给定余能密度函数和内变量演化方程推导出黏弹性本构方程.方程能包含经典黏弹性模型的本构方程,而且可描述材料的非线性黏弹性变形.对本构方程所基于的基本热力学方程性质进行讨论,表明在约束构型空间中热力学力和内变量之间要满足一定的共轭关系,所建构的本构方程才能刻画材料的黏弹性变形行为;证明了在约束构型空间中流动势函数随时间单调递减;同时指出在统计力学层面流动势函数与表征材料状态的概率密度函数有关.Viscoelasticity exists widely in various materials, such as asphalt concrete and polymer, and is also an important part of time-dependent deformation of rock materials. Based on Rice irreversible thermodynamics, the viscoelasticity of material is discussed. A set of scalar internal state variable is introduced to characterize the structural rearrangement in material sample, and the general viscoelastic constitutive equation is derived by giving specific complementary energy function and kinetic law of internal state variables. The proposed equation covers constitutive equation from classical viscoelastic models, can describe nonlinear viscoelasticity scenes. The properties of fundamental thermodynamic function, on which the proposed constitutive equation is based, are analyzed. We point out the special conjugate relation between thermodynamic forces and internal state variable, prove the flow potential function has monotonic decreasing with time in constrained conjugate space, and indicate that flow potential relates to probability of states of material in statistical mechanics level.

关 键 词：内变量热力学 黏弹性 本构方程 流动势函数 

分 类 号：O341[理学—固体力学]