# Book:A.J.M. Spencer/Continuum Mechanics

## A.J.M. Spencer: Continuum Mechanics

Published $\text {1980}$, Dover Publications

ISBN 0-486-43594-6.

### Contents

Preface
1: Introduction
1.1 Continuum mechanics
2: Introductory matrix algebra
2.1 Matrices
2.2 The summation convention
2.3 Eigenvalues and eigenvectors
2.4 The Cayley-Hamilton Theorem
2.5 The polar decompositon theorem
3: Vectors and cartesian tensors
3.1 Vectors
3.2 Coordinate transformations
3.4 Cartesian tensors
3.5 Isotropic tensors
3.6 Multiplication of tensors
3.7 Tensor and matrix notation
3.8 Invariants of a second-order tensor
3.9 Deviatoric tensors
3.10 Vector and tensor calculus
4: Particle kinematics
4.1 Bodies and their configurations
4.2 Displacement and velocity
4.3 Time rates of change
4.4 Acceleration
4.5 Steady motion. Particle paths and streamlines
4.6 Problems
5: Stress
5.1 Surface traction
5.2 Components of stress
5.3 The traction on any surface
5.4 Transformation of stress components
5.5 Equations of equilibrium
5.6 Principal stress components, principal axes of stress
5.7 The stress deviator tensor
5.8 Shear stress
5.9 Some simple states of stress
5.10 Problems
6: Motions and deformations
6.1 Rigid-body motions
6.2 Extension of a material line element
6.4 Finite deformation and strain tensors
6.5 Some simple finite deformations
6.6 Infinitesimal strain
6.7 Infinitesimal rotation
6.8 The rate-of-deformation tensor
6.9 The velocity gradient and spin tensors
6.10 Some simple flows
6.11 Problems
7: Conservation laws
7.1 Conservation laws of physics
7.2 Conservation of mass
7.3 The material time derivative of a volume integral
7.4 Conservation of linear momentum
7.5 Conservation of angular momentum
7.6 Conservation of energy
7.7 The principle of virtual work
7.8 Problems
8: Linear constitutive equations
8.1 Constitutive equations and ideal materials
8.2 Material symmetry
8.3 Linear elasticity
8.4 Newtonian viscous fluids
8.5 Linear viscoelasticity
8.6 Problems
9: Further analysis of finite deformation
9.1 Deformation of a surface element
9.2 Decomposition of a deformation
9.3 Principal stretches and principal axes of deformation
9.4 Strain invariante
9.5 Alternative stress measures
9.6 Problems
10: Non-linear constitutive equations
10.1 Non-linear theories
10.2 The theory of finite elastic deformations
10.3 A non-linear viscous fluid
10.4 Non-linear viscoelasticity
10.5 Plasticity
10.6 Problems
11: Cylindrical and spherical polar coordinates
11.1 Curvilinear coordinates
11.2 Cylindrical polar coordinates
11.3 Spherical polar coordinates
11.4 Problems
Appendix. Representation theorem for an isotropic tensor function