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.

"This is a remarkable textbook on the mechanics of deformable solids pertaining to thermal intervention. ... The present work stands out for its phenomenological access to the subject in conjunction with the pertaining mathematical tools, the inductive art of tackling and exposing the arguments and for the elaboration of single tasks of general interest as well as of engineering relevance. The reader will find the text inspiring ... ." (Ioannis Doltsinis, Mathematical Reviews, March, 2019)

“This is a remarkable textbook on the mechanics of deformable solids pertaining to thermal intervention. … The present work stands out for its phenomenological access to the subject in conjunction with the pertaining mathematical tools, the inductive art of tackling and exposing the arguments and for the elaboration of single tasks of general interest as well as of engineering relevance. The reader will find the text inspiring … .” (Ioannis Doltsinis, Mathematical Reviews, March, 2019)