内参量热力学中的应变参量分析

AN ANALYSIS OF STRAIN VARIABLES IN THE THERMO DYNAMICS OF INTERNAL VARIABLES OF DEFORMATION BODIES

以连续体的各力学守恒定律和熵函数为基础,给出了完备的变形体内参量热力学的表述框架。讨论了将热力学状态参量分划为外参量和内参量的必要性和依据,论证了热力学内参量和非弹性变形的关系以及将各种类型的非弹性应变列为内参量的数学条件。给出了考虑非弹性变形的内参量热力学基本方程,讨论了熵平衡和熵产生的关系方程和行为特性。引入两种定义的变形体自由能函数的表述方程,给出了各相应的状态方程组。

A comprehensive expression for the thermodynamics of deformation bodies with internal state variables is developed on the bases of various conservation laws in continuum mechanics and the function of entropy. Equations for the balance of internal energy, i.e. the first law of thermodynamics, with different forms are worked out. The basis to distinguish the state variables of thermodynamics into two parts, i.e. external and internal variables, is discussed in detail, relations between the internal variables and the anelastic strains are expounded, and the mathematical basis of that the anelastic strain can be regarded as an internal variable is established. The basic equation for the thermodynamics of internal variables in consideration of the anelastic deformation is presented, and the relations of entropy balance and entropy production are esta(?)ished. Two different definitions for the functions of free energy (Helmboltz free energy or Gibbs free energy) and their expressions of thermodynamics with internal variables are developed, and the corresponding state equations which can give the relationships of stress, strain and temperature are provided.