Nonsmooth Mechanics and Analysis: Theoretical and Numerical Advances
Inthecourseofthelast?ftyyears, developmentsinnonsmoothana- sisandnonsmoothmechanicshaveoftenbeencloselylinked. Thepresent book acts as an illustration of this. Its objective is two-fold. It is of course intended to help to di?use the recent results obtained by various renownedspecialists. ButthereisanequaldesiretopayhomagetoJean Jacques Moreau, who is undoubtedly the most emblematic ?gure in the correlated, not to say dual, advances in these two ?elds. Jean Jacques Moreau appears as a rightful heir to the founders of di?erential calculus and mechanics through the depth of his thinking in the ?eld of nonsmooth mechanics and the size of his contribution to the development of nonsmooth analysis. His interest in mechanics has focused on a wide variety of subjects: singularities in ?uid ?ows, the initiation of cavitation, plasticity, and the statics and dynamics of gr- ular media. The ‘Ariadne’s thread’ running throughout is the notion of unilateral constraint. Allied to this is his investment in mathematics in the ?elds of convex analysis, calculus of variations and di?erential m- sures. When considering these contributions, regardless of their nature, one cannot fail to be struck by their clarity, discerning originality and elegance. Precision and rigor of thinking, clarity and elegance of style are the distinctive features of his work.
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adhesion admissible algorithm applications assume assumption ballast Bisegna boundary bounded Buttazzo classical Clausius-Duhem inequality collision compact complementarity cone consider constraints contact problems convergence convex analysis convex function convex hull convex set Coulomb's law Curnier Dacorogna defined denotes differential inclusion displacements dissipation dry friction dual duality elastic energy equivalent evolution existence Figure finite fluctuations fluid formulation Fremond given global minimizer gradient grains granular materials Hamilton-Jacobi theory impact impulse indicator function inequality initial integral interface J.J. Moreau Jean Jacques Moreau kinematic kinetic Lagrangian Lemma linear Lipschitz continuous Math Mathematics matrix measure Mecanique mechanics method metric space Newton's cradle nonlinear nonsmooth numerical obtained operator optimal Panagiotopoulos parameter particle plasticity Proof properties proximal mapping Raous Rockafellar satisfied scale shakedown simulations solution space static subgradient sweeping process Theorem theory tion unilateral contact unique values vector velocity voie