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

Subject Matter

 * Mechanics

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
* : $2.2$: The summation convention