Nonlinear Waves in Elastic Crystals

Hardcover | November 11, 1999

byGerard Maugin

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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 aselastic 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 thecrystal 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. Alarge 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.

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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 aselastic crystals) where the nonlinear effects co...

Gerard Maugin is at Universite Pierre et Marie Curie and CNRS, Paris.

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Format:HardcoverPublished:November 11, 1999Publisher:Oxford University PressLanguage:English

The following ISBNs are associated with this title:

ISBN - 10:0198534841

ISBN - 13:9780198534846

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Table of Contents

1. Different types of crystal2. Discrete and continuum descriptions: general introduction3. Elasticity and anelasticity: continuous viewpoint4. Elasticity and anelasticity: discrete viewpoint5. Coupled fields in elasticity6. Nonlinear waves in elastic chains7. Nonlinear waves in elastic crystals with a microstructure8. Nonlinear waves in martensitic structures9. Nonlinear acoustic surface waves on crystals10. Shock waves and phase-transition fronts in thermoelasticcrystals11. Miscellani12. Postface by way of conclusion

Editorial Reviews

' Whilst it is inevitably a mathematical text, it is cleary written and contains many diagrams to assist with visualisation of the computational results and concepts' Islib