Book:A.J.M. Spencer/Continuum Mechanics
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A.J.M. Spencer: Continuum Mechanics
Published $\text {1980}$, Dover Publications
- ISBN 0-486-43594-6
Subject Matter
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
- 3.3 The dyadic product
- 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
- 6.3 The deformation gradient tensor
- 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
- Answers
- Further reading
- Index
Source work progress
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