Virtual Work and Shape Change in Solid Mechanics

Introduction.- The System.- The Principle of Virtual Work.- What We See: the Velocities.- The Actions which are Applied to the System: the Work of the External Forces.- What We See: the Velocities of Deformation.- The Work to Change the Shape of the System.- The Work to Change the Velocities of the System.- The Principle of Virtual Work and the Equations of Motion.- Summary of the Abstract Setting to get the Equations of Motion.- Two Points on a Line.- Three Disks in a Plane.- Three Balls on a Plane.- A Deformable Solid.- Two Deformable Solids.- At a Distance Interactions: Continuum Reinforced by Fibers.- At a Distance Interactions: Continuum Reinforced by Beams.- At a Distance Interactions: Continuum Reinforced by Plates.- Damage of a Connection.- Damage of a Rod Glued on a Rigid Surface.- Damage of a Beam Glued on a Rigid Surface.- A Damageable Solid.- Two Damageable Solids.- Porous Solids.- Discontinuum Mechanics: Collisions and Fractures in Solids.- There is neither Flattening nor Self-contact or Contact with an Obstacle. Smooth Evolution.- There is neither Flattening nor Self-contact or Contact with an Obstacle. Non Smooth Evolution.- There is no Flattening. There is Self-contact and Contact with an Obstacle. Smooth Evolution.- There is no Flattening. There is Self-contact and Contact with an Obstacle. Non Smooth Evolution. Flattening. Smooth and Non Smooth Evolutions.- Conclusions.