Founders of non-smooth dynamics

Jean Jacques Moreau	and	Michelle Schatzman

Other people naturally can be added to the list of the founders, among them, in France, Jacques Louis Lions, Haim Brézis, and Roland Glowinski in maths, Georges Duvaut, Nguyen Quoc Son, Bernard Nayroles, Olivier Débordes, Michel Jean, Pierre Suquet in mechanics ...

Nonsmooth Mechanics

Roughly speaking, non-smooth dynamics is the branch of mechanics that deals with dynamical systems governed by non-smooth laws. Common examples are unilateral constraints, friction, impact, plasticity, damage, brittle failure, etc. My main theoretical interest in this area is the numerical aspect of the sweeping process. The sweeping process is a powerful concept, both mathematical and mechanical, introduced by Jean Jacques Moreau.

For more details on my current research program, you cna ahave a look to TRIPOP research program

Main topics

Main topics of research on Non Smooth Dynamical Systems (NSDS):

• Moreau's sweeping process and unbounded differential inclusions
• Complementarity systems, variational inequalities
• Higher order systems with unilateral constraints
• Nonsmooth Mechanics, multibody dynamics with contact, impact and friction : mechanisms, granular materials
• Nonsmooth Electronics, electrical circuits with ideal components
• Numerical time-integration of non-smooth dynamical systems
• Numerical solvers for discrete variational inequalities and complementarity for the 3D frictional contact problem and plasticity
• Non-convex and non-smooth constitutive laws of materials (coupling contact and friction with cohesion and surfacic damage)

Applications, valorization and transfer

• Specifications and development for the SICONOS Platform
• Virtual reality. Joint Work with the SIAMES project.
• Mechanisms of circuit breaker with shocks in collaboration with M. Abadie (Schneider Electric)
• Masonry structures and historical monuments (PhD Thesis), PhD Thesis

Useful literature for my research (must read)

• Moreau, J. J. (1966). Fonctionnelles convexes. Séminaire Jean Leray, (2), 1-108.
• Moreau, J. J. (1974). On unilateral constraints, friction and plasticity. In New variational techniques in mathematical physics (pp. 171-322). Berlin, Heidelberg: Springer Berlin Heidelberg. Hal version
• Moreau, J. J. (1988). Unilateral contact and dry friction in finite freedom dynamics. In Nonsmooth mechanics and Applications (pp. 1-82). Vienna: Springer Vienna. Hal version
• Moreau, J. J. (1987). Bounded variation in time. Topics in nonsmooth mechanics. Hal version
• Brezis, H. (1973). Operateurs maximaux monotones et semi-groupes de contractions dans les espaces de Hilbert. Math. Studies.
• Germain, P. (1973). Cours de mécanique des milieux continus. Masson
• Duvant, G., & Lions, J. L. (1976). Inequalities in mechanics and physics (Vol. 219). Springer Science & Business Media.
• Trémolieres, R., Lions, J. L., & Glowinski, R. (1981). Numerical analysis of variational inequalities. North Holland publishing company.
• Cottle, R. W., Pang, J. S., & Stone, R. E. (2009). The linear complementarity problem. Society for Industrial and Applied Mathematics.
• Facchinei, F & Pang J.S. (2003). Finite-dimensional variational inequalities and complementarity problems. Springer
• Hirriart-Urruty, J. B., & Lemaréchal, C. (1996). Convex analysis and minimization algorithms I: Fundamentals (Vol. 305). Springer science & business media.
• Rockafellar, R.T. (1973) Convex Analysis. Princeton University press
• Wilmanski, K. (2008). Continuum Thermodynamics-Part I: Foundations (Vol. 77). World Scientific. lecture notes

Old Favorite Links

SICONOS

• Bernard Brogliato
• Christoph Glocker other old link
• Non smooth mechanics team at LMGC (P. Alart,  Frédéric Dubois,  Farang Radjai)
• Claude-Henri Lamarque

Da Vinci: Differential Algebraic and Variational Inequalities in Control and Simulation

• David Stewart
• Florian Potra
• Jong-Shi Pang
• Jeffrey C. Trinkle
• Mihai Anitescu