【作者】 张晓敏；

【导师】 彭向和；

【作者基本信息】 重庆大学 ， 固体力学， 2006， 博士

【摘要】 高能量沉积和大温度梯度下的非稳态温度场及其耦合应力场的研究具有十分重要的理论意义和应用背景。它涉及与高能量沉积相关的一系列基本理论问题,如固体本构方程、多尺度问题、热力耦合波传播和非Fourier效应等,因而成为近代科学技术发展的重要环节,受到许多科学家和工程师的高度重视。本文从基础原理和基础理论出发,力图在线性理论的框架内对强热沉积下热力耦合问题的几个基础性问题进行较为深入的分析。全文共7章:第1章绪论,简要述评热力耦合问题的研究现状。第2章针对各类物质模型在本构谱系中地位与联系的表述问题,叙述热力耦合本构理论,在现代本构理论的谱系中给常用的热传导方程的各类形式,如Gurtin热传导物质、Cattanco物质、Fourier热传导物质和Jeffreys物质予相应的地位并归入相应的谱系。叙述中涉及了变形梯度、高阶变形梯度、温度、温度梯度和温升率描写的应力、偶应力和热流矢量。提出了热梯度物质模型及其特例,给出了本构方程的简化式和与标架无差异性相协调的表示定理。第3章第3.1节针对单纯热传导,讨论双相有限延迟型热传导介质的温度传播模式及其传播的群速度。证明群速度的最大值不等于CV模型相应的传播速度,而是其0.6065倍;并在3.2节中将Biot对Fourier介质的变分方程推广有限松弛-延迟型非Fourier介质的热传导问题,得到含双有限松弛时间的变分方程;对比地讨论了与微分型非Fourier介质对应变分方程,及其势函数形式;第3章第3.3节探讨双相有限延迟型热传导定律相应的热力耦合传播模式,由此导出热力耦合传播的两个彼此联系的群速度,即第一声和第二声,及其关联;第3.4节讨论有限松弛-延迟型非Fourier介质的热力耦合问题的变分方程,将第3.2节所述的热传导问题的变分方程推广到有限松弛-延迟型非Fourier介质热传导定律架构的热力耦合情况,得到包含了双有限松弛时间的变分方程;作为比较,还得到了微分型(CV型)非Fourier介质热传导定律构架的热力耦合情况的变分方程,并得到了它的势函数形式。作为应用,讨论了半空间在表面受恒温热冲击问题的近似解,得到含有松弛时间及相应的松弛尺寸参数的热影响区域与时间的指数函数增长关系。第4章针对热力耦合问题的解法问题,建议一个热力耦合问题的解耦迭代算法,即交替地计算两个解除了耦合的问题,逐步地得到足够精度的解;这两个问题分别是已知温度时空分布的热Hooke介质的应力分析问题和已知位移、应变和更多还原

【Abstract】 The research on the distributions of non-steady temperature and the coupled stress caused by the deposition of highly concentrated energy and the induced enormous temperature gradient is receiving increasing attention due to its important significance and engineering background. It involves a series of fundamental theoretical problems, such as constitutive relations of solids, multi-scale analysis, coupled thermo-mechanical wave propagation, and non-Fourier effect of heat conduction, etc. In this dissertation, some of its fundamental problems are to be investigated based on the fundamental thermo-mechanical principles and theories and within the framework of linear systems. There are seven chapters in this dissertation.In Chapter 1, the state of the art in the coupled thermal-mechanical problems is briefly reviewed.In Chapter 2, the status of different material models in the constitutive pedigree and the correlation between different material models are discussed. The conventional heat conduction laws of different materials, such as Gurtin heat conducting material, Cattanco material, Fourier thermal conduct material and Jeffreys material, are classified into the corresponding constitutive pedigrees. The involved deformation and its gradient, strain gradient, temperature gradient, heating rate, and their contribution to stress, couple stress and heat flux are also emphasized. The concept of a heat gradient material as well as one of its special cases is introduced.In Section 3.1 of Chapter 3, the concept of thermal gradient material and an example are presented. The heat conduction modes and the corresponding velocity group in a kind of dual-phase finite lag non-Fourier media are discussed. It proves that the maximum value in the velocity group is not equal to but 0.6065 times the velocity of CV model. In Section 3.2, the variation equation for Fourier media proposed by Biot is extended to the heat conduction of dual-phase-finite lag non-Fourier media, which leads to the variation equation with dual finite relaxation time. In contrast, the variation equation and potential function of a differential Non-Fourier media are discussed. In Section 3.3, the coupled thermal-mechanical transportation mode of dual-phase-finite lag non-Fourier media is discussed. Two groups of velocities in the coupled thermal-mechanical transportation, i.e., the first and the second velocities of sound and their correlation, are derived. In Section 3.4, the variation equation for a finite relaxation-lag更多还原