Author 
Frémond, M., author.

Series 
Springer series in solid and structural mechanics ; v. 7 

Springer series in solid and structural mechanics ;
7.

Subject 
Virtual work.


Mechanics.


Motion.

Genre/Form 
Electronic books. 
Alt Name 
Ohio Library and Information Network.

Description 
1 online resource (xvi, 371 pages). 
Bibliography Note 
Includes bibliographical references. 
Contents 
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 Selfcontact or Contact with an Obstacle. Smooth Evolution  There is neither Flattening nor Selfcontact or Contact with an Obstacle. Non Smooth Evolution  There is no Flattening. There is Selfcontact and Contact with an Obstacle. Smooth Evolution  There is no Flattening. There is Selfcontact and Contact with an Obstacle. Non Smooth Evolution. Flattening. Smooth and Non Smooth Evolutions  Conclusions. 
Summary 
This book provides novel insights into two basic subjects in solid mechanics: virtual work and shape change. When we move a solid, the work we expend in moving it is used to modify both its shape and its velocity. This observation leads to the Principle of Virtual Work. Virtual work depends linearly on virtual velocities, which are velocities we may think of. The virtual work of the internal forces accounts for the changes in shape. Engineering provides innumerable examples of shape changes, i.e., deformations, and of velocities of deformation. This book presents examples of usual and unusual shape changes, providing with the Principle of Virtual Work various and sometimes new equations of motion for smooth and nonsmooth (i.e., with collisions) motions: systems of disks, systems of balls, classical and nonclassical small deformation theories, systems involving volume and surface damage, systems with interactions at a distance (e.g., solids reinforced by fibers), systems involving porosity, beams with third gradient theory, collisions, and fracturing of solids. The final example of shape change focuses on the motion of solids with large deformations. The stretch matrix and the rotation matrix of the polar decomposition are chosen to describe the shape change. Observation shows that a third gradient theory is needed to sustain the usual external loads. The new equations of motion are complemented with constitutive laws. Assuming a viscoelastic behavior, a mathematically coherent new predictive theory of motion is derived. The results are extended to motion with smooth and nonsmooth selfcontact, collision with an obstacle, incompressibility, and plasticity. Extreme behaviors are sufficiently numerous to consider the parti pris that a material may flatten into a surface (e.g., flattening of a structure by a power hammer) or a curve (e.g., transformation of an ingot into a wire in an extruder). Flattening is an example of the importance of the spatial variation of the rotation matrix when investigating the motion of a solid. 
Access 
Available to OhioLINK libraries. 
Note 
Print version record. 
ISBN 
9783319406824 (electronic bk.) 

3319406825 (electronic bk.) 

3319406817 

9783319406817 
OCLC # 
959872751 
Additional Format 
Print version: Fremond, Michel. Virtual Work and Shape Change in Solid Mechanics. Cham : Springer International Publishing, ©2016 9783319406817 
