Introduction to Nonlinear Thermomechanics of Solids [Paperback]

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.

1. Introduction.- 1.1. General remarks on the book content.- 1.2. Nonlinear continuum thermomechanics as a field of research and its industrial applications.- 2. Fundamental concepts of mechanics.- 2.1. Statics of a bar.- 2.2. Trusses.- 2.3. Two-dimensional continuum generalization.- 3. Fundamentals of tensor algebra and analysis.- 3.1. Introduction.- 3.1.1. Euclidean space and coordinate systems.- 3.1.2. Scalars and vectors.- 3.1.3. Basis of vector space.- 3.2. Tensors.- 3.2.1. Definitions.- 3.2.2. Operations on tensors.- 3.2.3. Isotropic tensors.- 3.3. Second order tensors.- 3.3.1. Definitions and properties.- 3.3.2. Tensor eigenproblem.- 3.3.3. Spectral decomposition of symmetric tensor.- 3.3.4. Polar decomposition of tensor.- 3.4. Tensor functions and fields.- 3.4.1. Integration and differentiation of tensor fields.- 3.4.2. GaussOstrogradski theorem.- 3.5. Curvilinelã*