本文基于连续介质力学和理性扩展热力学分析流程,将L-S(Lord and Shulman)热弹性理论与声弹性理论相结合,建立L-S热声弹性理论的基本框架,包括运动学、力学与热力学、本构方程与演化方程、基本场方程四部分.在运动学部分,区分了 Lagrange描述和Euler描述,以及3种不同的状态和构形,同时针对热声弹性情况定义了两类从自然状态到初始状态的转变过程;在力学与热力学部分,给出了质量守恒定律、动量守恒定律、角动量守恒定律、能量守恒定律以及熵产不等式,从而引出经典不可逆热力学的局限性;在本构方程与演化方程部分,介绍了扩展不可逆热力学原理,并基于理性扩展热力学流程,推导了从自然状态到初始状态、从初始状态到最终状态的热声弹性本构方程与演化方程,将热流作为本构自变量并考虑了热流与应变和温度的相关性;在最后一部分给出了基本场方程的运动方程形式和适用于数值模拟的一阶速度-应力-热流-温度微分方程.
Theoretical Framework of L-S Thermoacoustoelasticity Based on Rational Extended Thermodynamics
This paper combines L-S thermoelasticity with acoustoelasticity based on continuum mechanics and analysis process of rational extended thermodynamics to establish the basic framework of L-S thermoacoustoelasticity,including four components:kinematics,mechanicsand thermodynamics,constitutive equations and evolution equations,and fundamental field equations.In the kinematic part,Lagrangian description and Eulerian description are distinguished,as well as three different states and configurations,while two types of transition processes from the natural state to the initial state are defined for the case of thermoacoustoelasticity;In the mechanics and thermodynamics part,the laws of conservation of mass,conservation of momentum,conservation of angular momentum,conservation of energy,and the entropy production inequality are given,which lead to the limitations of classical irreversible thermodynamics;In the part of the constitutive equations and evolution equations,the principle of extended irreversible thermodynamics is introduced,and the constitutive equations and evolution equations of thermoacoustoelasticity from the natural state to the initial state and those from the initial state to the final state are derived based on the process of rational extended thermodynamics,taking heat flux as the constitutive independent variable and considering the correlation of heat flux with strain and temperature;In the last part,the equations of motion and the first-order velocity-stress-heat flux-temperature differential equations for numerical simulations are given.
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