Virtual Work and Shape Change in Solid Mechanics

Michel Frémond

• Publisher: Springer
• Year: 2016
• Print ISBN:
  9783319406817
• eBook ISBN:
  9783319406824
• Topic: Physical Sciences
• Subtopic: Mechanics

This book provides novel insights into two fundamental subjects in solid mechanics: virtual work and shape change. The author explains how the principle of virtual work represents a tool for analysis of the mechanical effects of the evolution of the shape of a system, how it can be applied to observations and experiments, and how it may be adapted to produce predictive theories of numerous phenomena. The book is divided into three parts. The first relates the principle of virtual work to what we observe with our eyes, the second demonstrates its flexibility on the basis of many examples, and the third applies the principle to predict the motion of solids with large deformations. Examples of both usual and unusual shape changes are presented, and equations of motion, some of which are entirely new, are derived for smooth and non-smooth motions associated with, for instance, systems of disks, systems of balls, classical and non-classical small deformation theories, systems involving volume and surface damage, systems with interactions at a distance (e.g., solids reinforced by fibers), systems involving porosity, collisions, and fracturing of solids.

Table of contents

• Preface
• Contents
• Part I The Principle of Virtual Work
• 1 Introduction
• 2 The System
• 3 The Principle of Virtual Work
• 4 What We See: The Velocities
• 5 The Actions Which are Applied to the System: The Work of the External Forces
• 6 What We See: The Velocities of Deformation
• 7 The Work to Change the Shape of the System
• 8 The Work to Change the Velocities of the System
• 9 The Principle of Virtual Work and the Equations of Motion
• 10 Summary of the Abstract Setting to get the Equations of Motion
• Part II Examples
• 11 Introduction
• 12 Two Points on a Line
• 13 Three Disks in a Plane
• 14 Three Balls on a Plane
• 15 A Deformable Solid
• 16 Two Deformable Solids
• 17 At a Distance Interactions: Continuum Reinforced by Fibers
• 18 At a Distance Interactions: Continuum Reinforced by Beams
• 19 At a Distance Interactions: Continuum Reinforced by Plates
• 20 Damage of a Connection
• 21 Damage of a Rod Glued on a Rigid Surface
• 22 Damage of a Beam Glued on a Rigid Surface
• 23 A Damageable Solid
• 24 Two Damageable Solids
• 25 Porous Solids
• 26 Discontinuum Mechanics: Collisions and Fractures in Solids
• 27 Comments
• Part III Large Deformations
• 28 Introduction
• 29 The System
• 30 There Is Neither Flattening nor Self-contact or Contact with an Obstacle. Smooth Evolution
• 31 There Is Neither Flattening nor Self-contact or Contact with an Obstacle. Non Smooth Evolution
• 32 There Is No Flattening. There Is Self-contact and Contact with an Obstacle. Smooth Evolution
• 33 There Is No Flattening. There Is Self-contact and Contact with an Obstacle. Non Smooth Evolution
• 34 Flattening. Smooth and Non Smooth Evolutions
• 35 Conclusion
• Appendix A The 3times3 Matrices
• Appendix B Pseudo-Potential of Dissipation
• Appendix C Function of Dissipation