Virtual work and shape change in solid mechanics / Michel Frémond.
Fremond, Michel, author.
2017
QA831
Available Online

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Title Virtual work and shape change in solid mechanics / Michel Frémond.
Author Fremond, Michel, author.
ISBN 9783319406824 (electronic book)
3319406825 (electronic book)
3319406817
9783319406817
Publication Details Cham : Springer, ©2017.
Language English
Description 1 online resource (xvi, 371 pages).
Call Number QA831
Dewey Decimal Classification 531.23
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 non-smooth (i.e., with collisions) motions: 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, 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 non-smooth self-contact, 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.
Bibliography, etc. Note Includes bibliographical references.
Access Note Access limited to authorized users.
Source of Description Description based on print version record.
Series Springer series in solid and structural mechanics ; 7.
Available in Other Form Virtual Work and Shape Change in Solid Mechanics.
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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.

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