This book introduces thermomechanics mathematically. It progresses from an analysis of a simple bar with a force through various types of fundamental equation systems for thermomechanics. It explains how these fundamental equations can be used to derive a solution for a particular problem in the field. It explains both analytical and computational methods.

The book has 13 chapters. Chapter 1 introduces the book. Chapter 2 introduces the mechanics. It shows through examples how equations can be developed for stress, strain, force, and displacement using Hook’s law, and the geometry of solid structures. Chapter 3 is on tensor algebra, and explains the basics of tensors, including operations on tensors, multi-order tensors, decompositions of tensors, theorems on tensors, and tensors in curvilinear coordinate systems. The chapter ends with introducing absolute notation to describe tensors, where the description is independent of any particular coordinate system.

Chapters 4 through 8 develop a fundamental equation system of solid mechanics. A deformable body in motion has stresses, strains, displacements, and deformations at various points of time. First, the chapters show equations for strains and stresses. Then, they explain four related conservation laws: mass conservation law, momentum conservation law, angular momentum conservation law, and mechanical energy conservation law. The chapters also introduce material properties and equations governing these properties. They cover linear elasticity, hyperelasticity, hypoelasticity, viscoelasticity, and elastoplasticity. They develop constitutive equations relating stresses and strains for 1D, 2D, and 3D cases.

Chapter 8 integrates all of these equations to make a system of equations. It also introduces the boundary condition, and incremental forms of the continuity equations, the equations of motion, geometric equations, and the constitutive equations. The chapter ends by giving examples of how the system of equations can be used for deriving analytical solutions.

Chapters 9 to 11 are on thermomechanics. The chapters explain the first and second laws of thermodynamics, the heat conduction problem, and how to add their equations to the solid mechanics equations. They not only cover the fundamental equations, but also variational equations and discretization. They explain both linearity and non-linearity. The last chapter, on discretization, also refers to the weighted residual method apart from incremental approach-based methods. It explains how the formulations can be used to solve thermomechanics and solid mechanics problems with the aid of computers.

The last two chapters are on the finite element method (FEM). They introduce FEM for the heat conduction problem. They introduce various elements used in FEM such as 1D elements, constant strain elements, and isoparametric elements. They also explain how to use FEM for the linear algebraic system of equations by elimination and iterative methods. The chapters end with an explanation of how to solve differential equations with FEM.

The book has a chapter for introducing tensor algebra. It assumes that the readers understand matrices, vectors, differential calculus, integral calculus, and concepts of solid structures. The book is a good introduction for beginners who want to do research in solid mechanics and/or thermomechanics. It can be used as a textbook for courses involving solid mechanics/thermomechanics. For computer professionals dealing with engineering problems, this is a good introduction.