粘弹性体发展方程关于热力学广义坐标的精确解

Exact Solutions of Evolution Equation for Generalized Thermodynamic Coordinates of Viscoelastic Medium

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。对于热力学广义坐标的显解 ,当参加孤立系统熵增的坐标中存在一个中性稳态平衡坐标 ,并且 ,热力学广义力以阶跃函数给出时 ,精确解中将出现与时间成正比的项 ;当部分阳坐标参加孤立系统的熵增过程时 ,在相应的各精确解的表达式中 ,热力学广义力将被相当热力学广义力所代换 ,而相应显解的形式保持不变。

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) the term proportional to time will arise when only one neutrally stable equilibrium coordinate exists in the coordinates participating in the entropy production; and (2) the generalized thermodynamic forces will be replaced by the equivalent generalized thermodynamic forces when parts of the observed generalized thermodynamic coordinates participate in the entropy production.