Virtual Work and Shape Change in Solid Mechanics

Part I. The Principle of Virtual Work

1. Introduction
Michel Frémond

2. The System
Michel Frémond

3. The Principle of Virtual Work
Michel Frémond

4. What We See: The Velocities
Michel Frémond

5. The Actions Which are Applied to the System: The Work of the External Forces
Michel Frémond

6. What We See: The Velocities of Deformation
Michel Frémond

7. The Work to Change the Shape of the System
Michel Frémond

8. The Work to Change the Velocities of the System
Michel Frémond

9. The Principle of Virtual Work and the Equations of Motion
Michel Frémond

10. Summary of the Abstract Setting to get the Equations of Motion
Michel Frémond

Part II. Examples

11. Introduction
Michel Frémond

12. Two Points on a Line
Michel Frémond

13. Three Disks in a Plane
Michel Frémond

14. Three Balls on a Plane
Michel Frémond

15. A Deformable Solid
Michel Frémond

16. Two Deformable Solids
Michel Frémond

17. At a Distance Interactions: Continuum Reinforced by Fibers
Michel Frémond

18. At a Distance Interactions: Continuum Reinforced by Beams
Michel Frémond

19. At a Distance Interactions: Continuum Reinforced by Plates
Michel Frémond

20. Damage of a Connection
Michel Frémond

21. Damage of a Rod Glued on a Rigid Surface
Michel Frémond

22. Damage of a Beam Glued on a Rigid Surface
Michel Frémond

23. A Damageable Solid
Michel Frémond

24. Two Damageable Solids
Michel Frémond

25. Porous Solids
Michel Frémond

26. Discontinuum Mechanics: Collisions andFractures in Solids
Michel Frémond

27. Comments
Michel Frémond

Part III. Large Deformations

28. Introduction
Michel Frémond

29. The System
Michel Frémond

30. There Is Neither Flattening nor Self-contact or Contact with an Obstacle. Smooth Evolution
Michel Frémond

31. There Is Neither Flattening nor Self-contact or Contact with an Obstacle. Non Smooth Evolution
Michel Frémond

32. There Is No Flattening. There Is Self-contact and Contact with an Obstacle. Smooth Evolution
Michel Frémond

33. There Is No Flattening. There Is Self-contact and Contact with an Obstacle. Non Smooth Evolution
Michel Frémond

34. Flattening. Smooth and Non Smooth Evolutions
Michel Frémond

35. Conclusion
Michel Frémond

Keywords: Engineering, Continuum Mechanics and Mechanics of Materials, Classical Mechanics, Structural Mechanics, Engineering Design