偶应力热弹性介质控制方程的推导

Derivation of governing equations of couple-stress thermoelastic medium

非Fourier热传导的Lord-Shulman广义热弹性理论中包含了双曲型热传导方程,并且在广义热弹性介质中考虑了其微结构特性,引入了偶应力张量,偶应力研究可反映出材料的微尺度力学效应。文章基于LordShulman广义热弹性理论,从能量守恒定律出发,分析了偶应力热弹性介质中的运动平衡方程、本构方程、能量方程以及边界条件的推导过程,并由此获得偶应力热弹性介质的运动控制方程和温度控制方程具体形式。结果表明:与经典热弹性理论的控制方程相比,基于Lord-Shulman理论的偶应力热弹性介质控制方程中的机械场与温度场相互耦合,而且在温度控制方程中存在含有弛豫时间的项,可使热信号以波动的形式和有限速度传播;而且当偶应力材料参数和弛豫时间取为零时,控制方程退化为经典理论的形式。

With the consideration thermoelastic theory contains a h of non-fourier heat conduction, the Lord-Shulman generalized yperbolic heat conduction equation, and the couple-stress is introduced to reflect the effect of microscale and the microstructural characteristics of materials. Based on the Lord-Shulman generalized thermoelastic theory, the article analyzes the derivation of the motion equations, the constitutive equations, the energy equations and the boundary conditions in the couple- stress thermoelastic medium, obtaining the forms of motion governing equation and temperature governing equation. The results show that, compared with the governing equations of the classical theory, the ones based on Lord-Shulman theory in which the equations of the thermal field and the mechanical field are coupling with each other and the governing equations of temperature field contain the relaxation times item. So the propagation of thermal signal is in the form of fluctuation, and the velocity of it is finite, and the equations can also degenerate into the classical ones when letting the couple-stress constant and the relaxation time be zero.