Study On Coupled Thermomechanical Problems With Strong Heat Deposition

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...