This book exposes the general concepts and results concerning stability issues, especially for non-conservative systems. It then presents an approach of stability that is different from Lyapunov’s theory and leads to the second-order work criterion (which for historical reasons is also called Hill’s stability criterion). Thanks to the new concept of Kinematic Structural Stability, a complete equivalence between Lyapunov’s and Hill’s stability criteria 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-conservativity provide a full, fresh look at these fundamental questions. A special chapter is devoted to applications for granular systems.
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.
Jean Lerbet is Professor at University of Evry (University of Paris Saclay, France). He has been director of the Mechanical Engineering department for 12 years and currently co-responsible of the French Theoretical Mechanics Network. His two main research topics are geometry/mechanics and stability.
Noël Challamel is Professor at University of South Brittany in France, and head of a research team in Civil Engineering and Multiscale Mechanics. His research mainly concerns theoretical and applied mechanics (including structural mechanics), stability, vibrations and material modeling.
François Nicot is Research Professor at Grenoble-Alpes University (INRAE), France. His activities deal with geomechanics, with a special focus on micromechanics of granular materials and multiscale failure modeling. He is co-director of the International Research Network GeoMech and Editor-in-Chief of the European Journal of Environmental and Civil Engineering.
Félix Darve is Emeritus Professor at Grenoble-INP, University Grenoble Alpes, France. He is also co-editor of the International Journal for Numerical and Analytical Methods in Geomechanics. Earlier in his career, he was director of the School of Hydraulics and Mechanics Grenoble, of the national lab CNRS-GRECO “Géomatériaux” and of the European lab network ALERT “Geomaterials”. He has co-authored several books in geomechanics.
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