Mathematical Modeling in Continuum Mechanics

Temam and Miranville present core topics within the general themes of fluid and solid mechanics. The brisk style allows the text to cover a wide range of topics including viscous flow, magnetohydrodynamics, atmospheric flows, shock equations, turbulence, nonlinear solid mechanics, solitons, and the nonlinear Schrödinger equation. This second edition will be a unique resource for those studying continuum mechanics at the advanced undergraduate and beginning graduate level whether in engineering, mathematics, physics or the applied sciences. Exercises and hints for solutions have been added to the majority of chapters, and the final part on solid mechanics has been substantially expanded. These additions have now made it appropriate for use as a textbook, but it also remains an ideal reference book for students and anyone interested in continuum mechanics.

Topics include: viscous flow, magnetohydrodynamics, atmospheric flows, shock equations, turbulence, nonlinear solid mechanics and solitons.

Introduction; A few words about notations; Part I. Fundamental Concepts in Continuum Mechanics: 1. Describing the motion of a system: geometry and kinematics; 2. The fundamental law of dynamics; 3. The Cauchy stress tensor - applications; 4. Real and virtual powers; 5. Deformation tensor, deformation rate tensor, constitutive laws; 6. Energy equations and shock equations; Part II. Physics of Fluids: 7. General properties of Newtonian fluids; 8. Flows of inviscid fluids; 9. Viscous fluids and thermohydraulics; 10. Magnetohydrodynamics and inertial confinement of plasmas; 11. Combustion; 12. Equations of the atmosphere and of the ocean; Part III. Solid Mechanics: 13. The general equations of linear elasticity; 14. Classical problems of elastostatics; 15. Energy theorems - duality: variational formulations; 16. Introduction to nonlinear constitutive laws and to homogenization; 17. Nonlinear elasticity and an application to biomechanics; Part IV. Introduction to Wave Phenomena: 18. Linear wave equations in mechanics; 19. The soliton equation: the Kortewed-de Vries equation; 20. The nonlinear Schrödinger equation; Appendix; Hints for the exercises; References; Index.