Abstract

The aim of this article is to build a mathematical model to study the problem of generalized thermoelastic porous medium according to the Lord–Shulman model and refined multi-phase lags model. The medium is considered to be homogeneous, isotropic and porous, such that changes in the size of the fracture field are in two dimensions. Four ordinary differential equations of the modified couple stress of thermoelastic porous media are obtained instead of partial differential equations and they solved precisely. The harmonic wave analysis procedure is proposed to find systematically the appropriate solutions to the variables of stresses, displacements, the change in the temperature, and in the volume fraction field. The outcomes of the physical variables have been computed numerically and clarified graphically. The comparison between both refined multi-phase lags and Lord–Shulman models are carried out for particular values of distance and various values of thermal relaxation times. This article’s findings may be useful to many researchers and scientists in the subject of materials science, especially porous media, as well as those working on creating modern technological materials.

摘要

本文的目的是根据 Lord-Shulman 模型和精细的多相滞后模型建立数学模型来研究广义热弹性多孔介质问题。介质被认为是均匀的、各向同性的和多孔的，因此裂缝场的大小变化是二维的。得到了热弹性多孔介质修正耦合应力的四个常微分方程代替偏微分方程，并得到了精确求解。提出了谐波分析程序，以系统地找到应力、位移、温度变化和体积分数场变量的适当解。物理变量的结果已通过数字计算并以图形方式阐明。针对特定的距离值和各种热弛豫时间值，对精细多相滞后模型和 Lord-Shulman 模型进行了比较。本文的发现可能对材料科学领域的许多研究人员和科学家有用，尤其是多孔介质，以及那些致力于创造现代技术材料的人员。