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Full Description
Mechanics have played an important role in mathematics, from infinitesimal calculus, calculus of variations, partial differential equations and numerical methods (finite elements). Originally, mechanics treated smooth objects. Technological progress has evoked the necessity to model and solve more complicated problems, like unilateral contact and friction, plasticity, delamination and adhesion, advanced materials, etc. The new tools include convex analysis, differential calculus for convex functions, and subgradients of convex functions and extensions for nonconvex problems. Nonsmooth mechanics is a relatively complex field, and requires a good knowledge of mechanics and a good background in some parts of modern mathematics. The present volume of lecture notes follows a very successful advanced school, with the aim to cover as much as possible all these aspects. Therefore the contributions cover mechanical aspects as well as the mathematical and numerical treatment.
Contents
Collisions. Thermal effects. Collisions of deformable solids and collisions of solids and fluids.- An Introduction to Impacts.- Approximation of variational and hemivariational inequalities of elliptic type. Applications to contact problems with friction.- Semicoercive Hemivariational Inequalities, Regularization Methods, Applications on Mechanics.- Mathematical Programs with Equilibrium Constraints: Theory and Numerical Methods.- Applied Nonsmooth Mechanics of Deformable Bodies.
