Mechanics in Material Space with Applications to Defect and Fracture Mechanics

The aim of the book is to present, in a novel and unified fashion, the elements of Mechanics in Material Space or Configurational Mechanics, with applications to fracture and defect mechanics. This mechanics, in contrast to Newtonian mechanics in physical space, is concerned with defects such as cracks and dislocations, which are embedded in the material and might move in it. The level is kept accessible to any engineer, scientist or graduate student possessing some knowledge of calculus and partial differential equations, and working in the various areas where rational use of materials is essential.

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.- Conservation Laws for Inhomogeneous Bars under Arbitrary Axial Loading.- Appendix B.- B.1 Elastodynamics of Inhomogeneous Bernoulli-Euler Beams.- B.2 Reduction to Statics.- Appendix C.- C.1 Elastodynamics of Inhomogeneous Mindlin Plates.- C.2 Reduction to Statics.- References.- Symbol Index.- Author Index.