Book contents
- Frontmatter
- Contents
- Preface
- Acknowledgements
- Frequently used symbols
- 1 Introduction
- 2 Basic elements of linear elasticity
- 3 Methods
- 4 Green's functions for unit point force
- 5 Interactions between defects and stress
- 6 Inclusions in infinite homogeneous regions
- 7 Interactions between inclusions and imposed stress
- 8 Inclusions in finite regions – image effects
- 9 Inhomogeneities
- 10 Point defects in infinite homogeneous regions
- 11 Point defects and stress – image effects in finite bodies
- 12 Dislocations in infinite homogeneous regions
- 13 Dislocations and stress – image effects in finite regions
- 14 Interfaces
- 15 Interactions between interfaces and stress
- 16 Interactions between defects
- Appendix A Relationships involving the ∇ operator
- Appendix B Integral relationships
- Appendix C The tensor product of two vectors
- Appendix D Properties of the delta function
- Appendix E The alternator operator
- Appendix F Fourier transforms
- Appendix G Equations from the theory of isotropic elasticity
- Appendix H Components of the Eshelby tensor in isotropic system
- Appendix I Airy stress functions for plane strain
- Appendix J Deviatoric stress and strain in isotropic system
- References
- Index
2 - Basic elements of linear elasticity
- Frontmatter
- Contents
- Preface
- Acknowledgements
- Frequently used symbols
- 1 Introduction
- 2 Basic elements of linear elasticity
- 3 Methods
- 4 Green's functions for unit point force
- 5 Interactions between defects and stress
- 6 Inclusions in infinite homogeneous regions
- 7 Interactions between inclusions and imposed stress
- 8 Inclusions in finite regions – image effects
- 9 Inhomogeneities
- 10 Point defects in infinite homogeneous regions
- 11 Point defects and stress – image effects in finite bodies
- 12 Dislocations in infinite homogeneous regions
- 13 Dislocations and stress – image effects in finite regions
- 14 Interfaces
- 15 Interactions between interfaces and stress
- 16 Interactions between defects
- Appendix A Relationships involving the ∇ operator
- Appendix B Integral relationships
- Appendix C The tensor product of two vectors
- Appendix D Properties of the delta function
- Appendix E The alternator operator
- Appendix F Fourier transforms
- Appendix G Equations from the theory of isotropic elasticity
- Appendix H Components of the Eshelby tensor in isotropic system
- Appendix I Airy stress functions for plane strain
- Appendix J Deviatoric stress and strain in isotropic system
- References
- Index
Summary
Introduction
The basic elements of anisotropic linear elasticity are presented in concise form. First, the deformation of an elastically strained body is described in terms of the local displacements, strains, and rotations that occur throughout the body. Requirements on the strains that ensure compatibility of the medium are then described. Next, the forces acting throughout the body are described in terms of surface tractions, body forces, and stresses. Conditions for mechanical equilibrium are derived. The stresses and strains are then linearly coupled via elastic constants, and various stress–strain relationships are derived. Finally, the energy stored in an elastically strained medium is formulated. Elements of the theory for the special case when the medium is elastically isotropic are included, along with several formulations of additional elastic quantities required for treating crystal defects.
References include: Love (1944); Sokolnikoff (1946); Muskhelishvili (1953); Nye (1957); Lekhnitskii (1963); Bacon, Barnett and Scattergood (1979b); Soutas-Little (1999); Hetnarski and Ignaczak (2004) and Asaro and Lubarda (2006).
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- Publisher: Cambridge University PressPrint publication year: 2012