Introduction to Nonlinear Thermomechanics of Solids

The first part of this textbook presents the mathematical background needed to precisely describe the basic problem of continuum thermomechanics. The book then concentrates on developing governing equations for the problem dealing in turn with the kinematics of material continuum, description of the state of stress, discussion of the fundamental conservation laws of underlying physics, formulation of initial-boundary value problems and presenting weak (variational) formulations. In the final part the crucial issue of developing techniques for solving specific problems of thermomechanics is addressed. To this aim the authors present a discretized formulation of the governing equations, discuss the fundamentals of the finite element method and develop some basic algorithms for solving algebraic and ordinary differential equations typical of problems on hand. Theoretical derivations are followed by carefully prepared computational exercises and solutions.

Table of Contents

Chapter 1 Introduction
Chapter 2 Fundamental Concepts of Mechanics
Chapter 3 Fundamentals of Tensor Algebra and Analysis
Chapter 4 Motion, Deformation and Strain in Material Continuum
Chapter 5 Description of Stress State
Chapter 6 Conservation Laws in Continuum Mechanics
Chapter 7 Constitutive Equations
Chapter 8 Fundamental System of Solid Mechanics Equations
Chapter 9 Fundamentals of Thermomechanics and Heat Conduction Problem
Chapter 10 Variational Formulations in Solid Thermomechanics
Chapter 11 Discrete Formulations in Thermomechanics
Chapter 12 Fundamentals of Finite Element Method
Chapter 13 Solution of FEM Equation Systems