Material Inhomogeneities in Elasticity

Gerard Maugin is Director of Research at CNRS, Paris, and teacher at the Universite Pierre et Marie Curie (Paris VI), France.

• Preface -- 1 Newton's concept of physical force -- 1.1. Newton's viewpoint -- 1.2. D' Alembert's viewpoint -- 1.3. Point particles and continua 7 -- 1.4. The modern point of view: duality -- 1.5. Lagrange versus Euler -- 2 Eshelby's concept of material force -- 2.1. Ideas from solid state physics -- 2.2. Peach-Koehler force -- 2.3. Force on a singularity -- 2.4. Energy-release rate -- 2.5. Pseudomomentum -- 2.6. Relationship with phonon and photon physics -- 3 Essentials of nonlinear elasticity theory -- 3.1. Material continuum in motion -- 3.2. Elastic me����sures of strains -- 3.3. Compatibility of strains -- 3.4. Balance laws (Euler-Cauchy) -- 3.5. Balance laws (Piola-Kirchhoff) -- 3.6. Constitutive equations -- 3.7. Concluding remarks -- 4 Material balance laws and inhomogeneity -- 4.1. Fully material balance laws -- 4.2. Material inhomogeneity force and pseudomomentum -- 4.3. Interpretation of pseudomomentum -- 4.4. Four formulations of the balance of linear momentum -- 4.5. Other material balance laws -- 4.6. Comments -- 5 Elasticity as a field theory -- 5.1. Elements of field theory -- 5.2. Noether's theorem -- 5.3. Variational formulation (direct-motion description) -- 5.4. Variational formulation (inverse-motion description) -- 5.5. Other material balance laws -- 5.6. Canonical Hamiltonian formulation -- 5.7. Balance of total pseudomomentum -- 5.8. Nonsimple materals: second-gradient theory -- 5.9. Complementary-energy variational principle -- 5.10. Peach-Koehler force revisited -- 5.11. Concluding remarks -- 6 Geometrical aspects of elasticity theory -- 6.1. Material uniformity and inhomogeneity -- 6.2. Eshelby stress tensor -- 6.3. Covariant material balance law of momentum -- 6.4. Continuous distributions of dislocations -- 6.5. Variational formulation using two variations -- 6.6. Second-gradient theory -- 6.7. Continuous distributions of disclinations -- 6.8. Similarity to Einstein-Cartan gravitation theory -- 7 Material inhomogeneities and brittle fracture -- 7.1. The problem of fracture -- 7.2. Generalized Reynolds and Green-Gauss theorems -- 7.3. Global material force -- 7.4. J-integral in fracture -- 7.5. Dual I-integral in fracture -- 7.6. Variational inequality: fracture propagation criterion -- 7.7. Other material balance laws and related path-independent integrals -- 7.8. Remark on the dynamical case -- 8 Material forces in electromagnetoelasticity -- 8.1. Electromagnetic elastic solids -- 8.2. Reminder of electromagnetic equations -- 8.3. Material electromagnetic fields -- 8.4. Variational principles -- 8.5. Balance of pseudomomentum and material forces -- 8.6. Fracture in electroelasticity and magnetoelasticity -- 8.7. Geometrical aspects: material uniformity -- 8.8. Electric Peach-Koehler force -- 8.9. Example of application: piezoelectric ceramics -- 9 Pseudomomentum and quasi-particles -- 9.1. Pseudomomentum of photons and phonons -- 9.2. Electromagnetic pseudomomentum -- 9.3. Conservation laws in wave theory -- 9.4. Conservation laws in soliton theory -- 9.5. Sine-Gordon systems and topological solitons -- 9.6. Boussinesq crystal equation and pseudomomentum -- 9.7. Sine-Gordon-d'Alembert systems -- 9.8. Nonlinear Schrodinger and Zakharov systems -- 10 Material forces in anelastic materials -- 10.1. Internal variables and dissipation -- 10.2. Balance of pseudomomentum -- 10.3. Global material forces -- Bibliography and references -- Index .