粘弹性体发展方程中关于热力学广义力精确解

通过不可逆热力过程，可导出描述粘弹性行为的发展方程，且其精确解的性质在很大 程度上依赖于热力学广义坐标所决定的系数矩阵的性质，即中性稳定平衡坐标和参加孤立系统熵增过程坐标的状况。对于热力学广义力的显解，当无中性稳态平衡坐标或中性稳态平衡坐标只出现在热力学广义阳坐标中时，显解有相同的表达式，如果这时只有部分坐标参加孤立系统熵增时，显解表达式中将出现热力学广义坐标的加速度项；当只有一个中性稳态平衡坐标出现在阴坐标中且热力学广义坐标以阶跃函数给出时，在所有热力学广义坐标都参加孤立系统熵增的条件下，显解中将出现与时间成正比的项；当中性稳态平衡坐标出现在参加孤立系统熵增的阴坐标中时，在所有阳坐标和部分阴坐标参加孤立系统熵增而不考虑中性稳态平衡坐标的数目的条件下，显解中将出现热力学广义坐标的加速度项。

Evolution Equation of Viscoelastic Medium and Exact Solutions for Generalized Thermodynamic Forces

It is obvious that the exact solutions of the evolution equation, which is derived by regarding the deformation process of viscoelastic materials as an irreversible thermodynamic process, depend very much on the properties of their coefficient matrices. These matrices are usually affected by the nature of the generalized thermodynamic coordinates, which leads the solutions for the generalized thermodynamic coordinates to that: (1) under the condition that no neutrally stable equilibrium coordinates exist or they are only in the observed ones, the exact explicit solutions are in the same forms, furthermore the accelerative term will arise in the explicit solutions when parts of the coordinates participate in the entropy production; (2) under the condition that all the generalized thermodynamic coordinates participate in the entropy production, the term proportional to time will arise when only one neutrally stable equilibrium coordinate exists in the hidden ones and the generalized thermodynamic coordinates are given in the form of step function; (3) under the condition that the neutrally stable equilibrium coordinate exists in the hidden ones which participate in the entropy production, the accelerative term will arise in the explicit solutions when all of the observed coordinates and parts of the hidden ones participate in the entropy production regardless of the number of the neutrally stable equilibrium coordinates.