沿等压路径求解疏松材料Hugoniot关系的微分方程组及其求解

 根据固体材料的三项式物态方程和Grüneisen物态方程，导出了沿等压路径求解疏松材料冲击温度和压缩体积随初始密度变化的微分方程组。从体积的微分方程出发，在假定Wu-Jing参量为常数的前提下，导出了冲击压缩体积和体积-焓物态方程的Wu-Jing表达式。采用数值差分方法求解微分方程组，计算了疏松铜的冲击压缩特性，并与文献中部分实验数据进行了比较，特别强调了热电子对冲击压缩体积、冲击温度和Wu-Jing参数的贡献。还讨论了Grüneisen物态方程与Wu-Jing物态方程的内在联系及后者的适用范围。

Differential Equations and Their Solutions for Hugoniot Relation of Porous Materials along the Isobaric Path

Shock compression techniques can be applied to porous materials to reproduce thermodynamic states at high temperatures and high densities, and a lot of Hugoniot data were published in the past two decades. To investigate the intrinsic relationship between Hugoniot curves of dense metals and porous ones is of importance for development of more reasonable equation of state (EOS) models. In this paper, a set of differential equations, which relate the temperature and density of the shocked states along an isobaric path in p-V-T space to its initial densities of the porous material, is deduced from the traditional three-terms EOS and Grüneisen EOS of solids. The differential formula of Wu-Jing EOS and the analytic expression of the Wu-Jing variable (R_p) are given. It is emphasized that Wu-Jing EOS is resulted not only from the contribution of crystal vibration as traditionally considered but also from most of the thermal electron effects. The new differential equations are applied to porous copper, and the effects of the thermal electrons to shock temperature, compression density, and value of Wu-Jing variable are discussed. It shows that the existence of the thermal electrons will reduce the increase rate of R_p with decrease of density.