Nonlinear Waves in Elastic Crystals

The mathematical modelling of changing structures in materials is of increasing importance to industry where applications of the theory are found in subjects as diverse as aerospace and medicine. This book deals with aspects of the nonlinear dynamics of deformable ordered solids (known as elastic crystals) where the nonlinear effects combine or compete with each other. Physical and mathematical models are discused and computational aspects are also included. Different models are considered - on discrete as well as continuum scales - applying heat, electricity, or magnetism to the crystal structure and these are analysed using the equations of rational mechanics. In this way the student is introduced to the important equations of nonlinear science that describe shock waves, solitons and chaos and also the non-exactly integrable systems or partial differential equations. A large number of problems and examples are included, many taken from recent research and involving both one-dimensional and two-dimensional problems as well as some coupled degress of freedom.

1. Different types of crystal; 2. Discrete and continuum descriptions: general introduction; 3. Elasticity and anelasticity: continuous viewpoint; 4. Elasticity and anelasticity: discrete viewpoint; 5. Coupled fields in elasticity; 6. Nonlinear waves in elastic chains; 7. Nonlinear waves in elastic crystals with a microstructure; 8. Nonlinear waves in martensitic structures; 9. Nonlinear acoustic surface waves on crystals; 10. Shock waves and phase-transition fronts in thermoelastic; crystals; 11. Miscellani; 12. Postface by way of conclusion