Mathematical Modelling in Continuum Mechanics (Hardcover)

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. Shock equations; Part II. Physics of Fluids: 7. General properties of Newtonian fluids; 8. Flows of perfect 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; Part IV. Introduction to Wave Phenomena: 17. Linear wave equations in mechanics; 18. The soliton equation: the Korteweg-de Vries equations; 19. The nonlinear Schrodinger equation; Appendix A.