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Nonsmooth Mechanics and Analysis

Theoretical and Numerical Advances

  • P. Alart
  • O. Maisonneuve
  • R. T. Rockafellar

Part of the Advances in Mechanics and Mathematics book series (AMMA, volume 12)

Table of contents

  1. Front Matter
    Pages i-xiv
  2. Convex and Nonsmooth Analysis

  3. Nonsmooth Mechanics

    1. Front Matter
      Pages 59-59
    2. L. -E. Andersson, A. Klarbring, J. R. Barber, M. Ciavarella
      Pages 61-70
    3. Michel Raous
      Pages 93-105
    4. Georgios E. Stavroulakis, Marek Engelhardt, Heinz Antes
      Pages 119-128
    5. Michelle Schatzman
      Pages 129-143
    6. Franco Maceri, Paolo Bisegna
      Pages 145-159
  4. Fluid Mechanics

    1. Front Matter
      Pages 161-161
    2. Jens Eggers
      Pages 163-172
  5. Multibody Dynamics: Numerical Aspects

    1. Front Matter
      Pages 183-183
    2. Christoph Glocker, Ueli Aeberhard
      Pages 185-194
    3. Pierre Alart, David Dureisseix, Mathieu Renouf
      Pages 195-207
    4. Michel Jean
      Pages 209-220
    5. Catherine Cholet, Gilles Saussine, Pierre-Etienne Gautier, Louis-Marie Cléon
      Pages 221-232
    6. Farhang Radjaï, Stéphane Roux
      Pages 233-245
  6. Topics in Nonsmooth Science

    1. Front Matter
      Pages 247-247
    2. Jean-Pierre Aubin, José Alberto Murillo Hernández
      Pages 249-259
    3. Vincent Acary, Bernard Brogliato
      Pages 261-277
    4. Manuel D. P. Monteiro Marques, Laetitia Paoli
      Pages 279-288
    5. Samir Adly, Hedy Attouch, Alexandre Cabot
      Pages 289-304
  7. Back Matter
    Pages 315-320

About these proceedings

Introduction

This book’s title, Nonsmooth Mechanics and Analysis, refers to a major domain of mechanics, particularly those initiated by the works of Jean Jacques Moreau. Nonsmooth mechanics concerns mechanical situations with possible nondifferentiable relationships, eventually discontinuous, as unilateral contact, dry friction, collisions, plasticity, damage, and phase transition. The basis of the approach consists in dealing with such problems without resorting to any regularization process. Indeed, the nonsmoothness is due to simplified mechanical modeling; a more sophisticated model would require too large a number of variables, and sometimes the mechanical information is not available via experimental investigations. Therefore, the mathematical formulation becomes nonsmooth; regularizing would only be a trick of arithmetic without any physical justification.

Nonsmooth analysis was developed, especially in Montpellier, to provide specific theoretical and numerical tools to deal with nonsmoothness. It is important not only in mechanics but also in physics, robotics, and economics.

 

Audience

This book is intended for researchers in mathematics and mechanics.

Keywords

Simulation calculus fluid mechanics mechanics modeling plasticity robot robotics

Editors and affiliations

  • P. Alart
    • 1
  • O. Maisonneuve
    • 1
  • R. T. Rockafellar
    • 2
  1. 1.Université Montpellier IIMontpellierFrance
  2. 2.University of WashingtonSeattleUSA

Bibliographic information