Mathematical Modeling in Continuum Mechanics

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.