Mechanics in Material Space

1 Mathematical Preliminaries.- 1.1 General Remarks.- 1.2 What is a Conservation Law?.- 1.3 Trivial Conservation Laws.- 1.4 System with a Lagrangian; Noether's Method.- 1.5 System without a Lagrangian; Neutral-Action Method.- 1.6 Discussion.- 2 Linear Theory of Elasticity.- 2.1 General Remarks.- 2.2 Elements of Linear Elasticity.- 2.3 Conservation Laws of Linear Elastostatics.- 2.4 Alternative Derivations of Conservation Laws.- 3 Properties of the Eshelby Tensor.- 3.1 General Remarks 81.- 3.2 Physical Interpretation of the Components of the Eshelby Tensor.- 3.3 Invariants, Principal Values, Principal Directions and Extremal Values of the Eshelby Tensor.- 4 Linear Elasticity with Defects.- 4.1 General Remarks.- 4.2 Path-Independent Integrals and Energy-Release Rates.- 4.3 Example: Hole-Dislocation Interaction.- 4.4 Path-Independent Integrals of Fracture Mechanics.- 5 Inhomogeneous Elastostatics.- 5.1 General Remarks.- 5.2 Symmetry Transformations.- 5.3 The Homogeneous Case.- 5.4 The Inhomogeneous Case.- 5.5 Relation to Stress-Intensity Factors.- 5.6 Examples.- 6 Elastodynamics.- 6.1 General Remarks.- 6.2 Time t as an Additional Independent Variable.- 6.3 Convolution in Time.- 6.4 Domain-Independent Integrals.- 6.5 Energy-Release Rates.- 6.6 Wave Motion.- 7 Dissipative Systems.- 7.1 General Remarks.- 7.2 Diffusion Equation.- 7.3 Non-Linear Wave Equation.- 7.4 Viscoelasticity.- 8 Coupled Fields.- 8.1 General Remarks.- 8.2 Piezoelectricity.- 8.3 Thermoelasticity.- 8.4 Mechanics of a Porous Medium.- 9 Bars, Shafts and Beams.- 9.1 General Remarks.- 9.2 Elements of Strength-of-Materials.- 9.3 Balance and Conservation Laws for Bars and Shafts.- 9.4 Balance and Conservation Laws for Beams.- 9.5 Energy-Release Rates and Stress-Intensity Factors.- 9.6 Examples.- 10 Plates and Shells.- 10.1 General Remarks.- 10.2 Plate Theories.- 10.3 Conservation Laws for Elastostatics of Mindlin Plates.- 10.4 Reduction to the Classical Theory.- 10.5 Conservation Laws for Shells.- Appendix A.-