Stability of Discrete Non-conservative Systems

Stability of Discrete Non-conservative Systems

1st Edition - November 16, 2020

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  • Authors: Jean Lerbet, Noel Challamel, Francois Nicot, Felix Darve
  • Hardcover ISBN: 9781785482861
  • eBook ISBN: 9780081027653

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Stability of Discrete Non-conservative Systems first exposes the general concepts and results concerning stability issues. It then presents an approach of stability that is different from Lyapunov which leads to the second order work criterion. Thanks to the new concept of Kinematic Structural Stability, a complete equivalence between two approaches of stability is obtained for a divergent type of stability. Extensions to flutter instability, to continuous systems, and to the dual questions concerning the measure of non-conservativeness provides a full, fresh look at these fundamental questions. A special chapter is devoted to applications for granular systems.

Key Features

  • Presents a structured review on stability questions
  • Provides analytical methods and key concepts that may be used in non-conservative frameworks like hypoelasticity


Researchers and Engineers in the large field of Solid Mechanics (Rational Mechanics, Structural mechanics, Granular Material, Elasticity, Plasticity, Fluid Structure Interactions) and in the field of Applied Mathematics

Table of Contents

  • Introduction
    1. On Stability of Discrete and Asymptotically Continuous systems
    2. Second-order work criterion and stability in the small
    3. Mixed perturbations and Second-order work criterion
    4. Divergence kinematic structural stability
    5. Flutter kinematic structural stability
    6. Geometric degree of non-conservativity
    7. Buckling of granular systems with shear interactions: Discrete versus continuum approaches
    8. Continuous Divergence KISS

Product details

  • No. of pages: 290
  • Language: English
  • Copyright: © ISTE Press - Elsevier 2020
  • Published: November 16, 2020
  • Imprint: ISTE Press - Elsevier
  • Hardcover ISBN: 9781785482861
  • eBook ISBN: 9780081027653

About the Authors

Jean Lerbet

Jean Lerbet holds a Master in Theoretical Mechanics of UPMC and a PHD in Theoretical Mechanics of UPMC. Since 2006 , he is the director of the Mechanical Engineering Department of Evry Val D’Essonne University . He is Co-responsable of the French Theoretical Mechanics Network since 2011 and Co-organizer of yearly Quiberon’s Summer Schools of Theoretical Mechanics. Also, responsable of Research Teams VASCO and SIMOB of IBISC Laboratory until 2018. During the first 15 years of his career , his main research topic dealt with the applications of calculations on Lie groups to mechanics. These researches led for example to the full classification of the Mechanisms. 
Since 2004, he focuses a main part of these researches to issues on Stability of Non-Conservative Systems. A major result is the full explanation of the links between two different criteria of stability thanks to the new concept of Kinematical Structural Stability which is the object of the present book.
 Other interest topics leading also to collaborations are geometrical aspects and/or mechanical applications of control theory, cohomological calculations or even deep learning.

Affiliations and Expertise

Professor, University of Evry, Paris Saclay University

Noel Challamel

Noël Challamel is Professor at University of South Brittany (Université de Bretagne Sud – Lorient, France). He is the head of a research team in Civil Engineering and Multiscale Mechanics. His research at University of South Brittany mainly concerns civil engineering, theoretical and applied mechanics problems, with a particular emphasis on scale effects, structural mechanics, stability, vibrations and material modeling (Continuum Damage Mechanics and Plasticity). He is the co- author of three books in the field of mechanics and civil engineering. He has published over a hundred papers in high standard journals. He is often consulted as a referee in more than 50 international journals in Civil Engineering, Physics or Mechanics. He is member of the editorial board of 11 international journals, and is associate editor of the Journal of Engineering Mechanics, one of the leading journals published by the American Society of Civil Engineering. He is also editor and head of the collection « Solid Mechanics and Mechanical Engineering » published by ISTE Wiley

Affiliations and Expertise

Professor, South Brittany University, France

Francois Nicot

François Nicot is a graduate from « Centrale de Lyon »school. He joined Cemagref (now IRSTEA) in 2000, where he currently works as Research Director. He has been Editor-in-Chief of the international journal "European Journal of Environmental and Civil Engineering" since 2009, and co-directs the GDRI (international research group) GeoMech since 2008. Author of more than 150 international publications, his research focuses on the geomechanics and behavior of granular materials.

Affiliations and Expertise

Research Director at IRSTEA, Grenoble, France

Felix Darve

Felix Darve obtained his Master's degree from Ecole Centrale Paris (1971), followed by a PhD in Grenoble (1978) on the constituent relations of geomaterials. He was promoted professor of exceptional rank at the Polytechnic Institute of Grenoble. He is former director of the National School of Hydraulics and Mechanics of Grenoble, the national laboratory of CNRS GRECO "Geomaterials" and the European network of laboratories ALERT "Geomaterials". He was deputy director of the department "Mechanics" at the Ministry of Research. Currently, F. Darve is editor-in-chief of Int. J. Num. and Anal. Meth. In geomechanics (Wiley publ.). He has edited or co-edited 14 books, published by Elsevier, Springer, Hermes, Iste, Balkema, ... and has written or co-authored 260 articles in peer-reviewed journals or book chapters. His three main topics of interest are (i) the development of incrementally non-linear constitutive relationships, (ii) the analysis of bifurcations, instabilities and failures in granular materials and (iii) the modeling of three-phase granular media.

Affiliations and Expertise

Emeritus Professor, University of Grenoble-Alpes, France

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