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Virtual Work and Shape Change in Solid Mechanics

  • Book
  • © 2017

Overview

Authors:
  1. Michel Frémond

    1. University of Rome Tor Vergata , Rome, Italy

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  • 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
  • Applies the principle of work to predict the motion of solids with large deformations
  • Includes examples of both usual and unusual shape changes
  • Derives equations for smooth and nonsmooth motions
  • Includes supplementary material: sn.pub/extras

Part of the book series: Springer Series in Solid and Structural Mechanics (SSSSM, volume 7)

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Table of contents (35 chapters)

  1. Front Matter

    Pages i-xvii
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  2. The Principle of Virtual Work

    1. Front Matter

      Pages 1-1
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    2. Introduction

      • Michel Frémond
      Pages 3-3

    3. The System

      • Michel Frémond
      Pages 5-5

    4. The Principle of Virtual Work

      • Michel Frémond
      Pages 7-8

    5. What We See: The Velocities

      • Michel Frémond
      Pages 9-12

    6. The Actions Which are Applied to the System: The Work of the External Forces

      • Michel Frémond
      Pages 13-14

    7. What We See: The Velocities of Deformation

      • Michel Frémond
      Pages 15-18

    8. The Work to Change the Shape of the System

      • Michel Frémond
      Pages 19-21

    9. The Work to Change the Velocities of the System

      • Michel Frémond
      Pages 23-26

    10. The Principle of Virtual Work and the Equations of Motion

      • Michel Frémond
      Pages 27-30

    11. Summary of the Abstract Setting to get the Equations of Motion

      • Michel Frémond
      Pages 31-31

  3. Examples

    1. Front Matter

      Pages 33-33
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    2. Introduction

      • Michel Frémond
      Pages 35-36

    3. Two Points on a Line

      • Michel Frémond
      Pages 37-39

    4. Three Disks in a Plane

      • Michel Frémond
      Pages 41-45

    5. Three Balls on a Plane

      • Michel Frémond
      Pages 47-51

    6. A Deformable Solid

      • Michel Frémond
      Pages 53-80

    7. Two Deformable Solids

      • Michel Frémond
      Pages 81-83

    8. At a Distance Interactions: Continuum Reinforced by Fibers

      • Michel Frémond
      Pages 85-87
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Keywords

About this book

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.

Reviews

“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)​

Authors and Affiliations

  • University of Rome Tor Vergata , Rome, Italy

    Michel Frémond

Bibliographic Information

  • Book Title: Virtual Work and Shape Change in Solid Mechanics

  • Authors: Michel Frémond

  • Series Title: Springer Series in Solid and Structural Mechanics

  • DOI: https://doi.org/10.1007/978-3-319-40682-4

  • Publisher: Springer Cham

  • eBook Packages: Engineering, Engineering (R0)

  • Copyright Information: Springer International Publishing Switzerland 2017

  • Hardcover ISBN: 978-3-319-40681-7Published: 04 October 2016

  • Softcover ISBN: 978-3-319-82153-5Published: 14 June 2018

  • eBook ISBN: 978-3-319-40682-4Published: 24 September 2016

  • Series ISSN: 2195-3511

  • Series E-ISSN: 2195-352X

  • Edition Number: 1

  • Number of Pages: XVII, 371

  • Number of Illustrations: 17 b/w illustrations

  • Topics: Solid Mechanics, Classical Mechanics, Solid Mechanics, Engineering Design

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