| |
| |
| Preface | |
| |
| |
| |
| Introduction | |
| |
| |
| |
| Continuum mechanics | |
| |
| |
| |
| Introductory matrix algebra | |
| |
| |
| |
| Matrices | |
| |
| |
| |
| The summation convention | |
| |
| |
| |
| Eigenvalues and eigenvectors | |
| |
| |
| |
| The Cayley-Hamilton theorem | |
| |
| |
| |
| The polar decomposition theorem | |
| |
| |
| |
| Vectors and cartesian tensors | |
| |
| |
| |
| Vectors | |
| |
| |
| |
| Coordinate transformations | |
| |
| |
| |
| The dyadic product | |
| |
| |
| |
| Cartesian tensors | |
| |
| |
| |
| Isotropic tensors | |
| |
| |
| |
| Multiplication of tensors | |
| |
| |
| |
| Tensor and matrix notation | |
| |
| |
| |
| Invariants of a second-order tensor | |
| |
| |
| |
| Deviatoric tensors | |
| |
| |
| |
| Vector and tensor calculus | |
| |
| |
| |
| Particle kinematics | |
| |
| |
| |
| Bodies and their configurations | |
| |
| |
| |
| Displacement and velocity | |
| |
| |
| |
| Time rates of change | |
| |
| |
| |
| Acceleration | |
| |
| |
| |
| Steady motion. Particle paths and streamlines | |
| |
| |
| |
| Problems | |
| |
| |
| |
| Stress | |
| |
| |
| |
| Surface traction | |
| |
| |
| |
| Components of stress | |
| |
| |
| |
| The traction on any surface | |
| |
| |
| |
| Transformation of stress components | |
| |
| |
| |
| Equations of equilibrium | |
| |
| |
| |
| Principal stress components, principal axes of stress and stress invariants | |
| |
| |
| |
| The stress deviator tensor | |
| |
| |
| |
| Shear stress | |
| |
| |
| |
| Some simple states of stress | |
| |
| |
| |
| Problems | |
| |
| |
| |
| Motions and deformations | |
| |
| |
| |
| Rigid-body motions | |
| |
| |
| |
| Extension of a material line element | |
| |
| |
| |
| The deformation gradient tensor | |
| |
| |
| |
| Finite deformation and strain tensors | |
| |
| |
| |
| Some simple finite deformations | |
| |
| |
| |
| Infinitesimal strain | |
| |
| |
| |
| Infinitesimal rotation | |
| |
| |
| |
| The rate-of-deformation tensor | |
| |
| |
| |
| The velocity gradient and spin tensors | |
| |
| |
| |
| Some simple flows | |
| |
| |
| |
| Problems | |
| |
| |
| |
| Conservation laws | |
| |
| |
| |
| Conservation laws of physics | |
| |
| |
| |
| Conservation of mass | |
| |
| |
| |
| The material time derivative of a volume integral | |
| |
| |
| |
| Conservation of linear momentum | |
| |
| |
| |
| Conservation of angular momentum | |
| |
| |
| |
| Conservation of energy | |
| |
| |
| |
| The principle of virtual work | |
| |
| |
| |
| Problems | |
| |
| |
| |
| Linear constitutive equations | |
| |
| |
| |
| Constitutive equations and ideal materials | |
| |
| |
| |
| Material symmetry | |
| |
| |
| |
| Linear elasticity | |
| |
| |
| |
| Newtonian viscous fluids | |
| |
| |
| |
| Linear viscoelasticity | |
| |
| |
| |
| Problems | |
| |
| |
| |
| Further analysis of finite deformation | |
| |
| |
| |
| Deformation of a surface element | |
| |
| |
| |
| Decomposition of a deformation | |
| |
| |
| |
| Principal stretches and principal axes of deformation | |
| |
| |
| |
| Strain invariants | |
| |
| |
| |
| Alternative stress measures | |
| |
| |
| |
| Problems | |
| |
| |
| |
| Non-linear constitutive equations | |
| |
| |
| |
| Non-linear theories | |
| |
| |
| |
| The theory of finite elastic deformations | |
| |
| |
| |
| A non-linear viscous fluid | |
| |
| |
| |
| Non-linear viscoelasticity | |
| |
| |
| |
| Plasticity | |
| |
| |
| |
| Problems | |
| |
| |
| |
| Cylindrical and spherical polar coordinates | |
| |
| |
| |
| Curvilinear coordinates | |
| |
| |
| |
| Cylindrical polar coordinates | |
| |
| |
| |
| Spherical polar coordinates | |
| |
| |
| |
| Problems | |
| |
| |
| |
| Representation theorem for an isotropic tensor function | |
| |
| |
| Answers | |
| |
| |
| Further reading | |
| |
| |
| Index | |