CONTINUUM MECHANICS

by Konstantin Z. Markov

"St. Kliment Ohridski'' University Press, Sofia, 2003, in press, 252 pages, ISBN 954-07-1768-X

CONTENTS

Chapter 1. Tensor Algebra

1. Vectors - direct and component definitions
2. Second rank tensors - direct and component definitions
3. Second rank tensors. Basic properties and operations
4. Functions of tensors. Polar decomposition
5. Example - the Euler tensor of inertia
6. Example - the Cauchys tensor of stresses
7. Higher ranks tensors
8. Symmetry group of a tensor. Isotropic tensors

Chapter 2. Tensor Calculus

9. Curvilinear coordinate systems
10. Vector and tensor fields - direct and component definitions
11. Vector and tensor analysis. Nabla-calculus
12. Differential operations in curvilinear coordinates
13. The Cristoffell symbols

Chapter 3. Kinematics of Continua

14. The notion and basic hypotheses of a continuum medium
15. Motion of continua - the Euler and Lagrange descriptions
16. Strain tensor
17. The compatibility equations of Saint Venant
18. Strain-rate tensor

Chapter 4. Fundamental Laws of Continunuum Mechanics

19. Continuity equation
20. The Euler axioms. Balance of linear momentum
21. Balance of angular momentum
22. Balance of kinetic energy
23. First law of thermodynamics

Chapter 5. Classical Models of Continua

24. Constitutive equations
25. Elastic solids. The Lame equations
26. The Lame problem
27. Ideal fluids. The Euler equations
28. The D'Alambert paradox
29. The Bernoulli integral
30. Viscous fluids. The Navier-Stokes equations
31. Simplest viscous flows
32. Slow flow past a rigid sphere. The Stokes formula