Stability of Discrete Non-conservative Systems

Jean Lerbet is Professor at the Universities of Evry and Paris Saclay in France. His research interests include differential geometry and mechanics, and stability. 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 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. 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.

• Introduction1. On Stability of Discrete and Asymptotically Continuous systems2. Second-order work criterion and stability in the small3. Mixed perturbations and Second-order work criterion4. Divergence kinematic structural stability5. Flutter kinematic structural stability6. Geometric degree of non-conservativity 7. Buckling of granular systems with shear interactions: Discrete versus continuum approaches8. Continuous Divergence KISSIndex