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This unique volume presents the state of the art in the field of multiscale modeling in solid mechanics, with particular emphasis on computational approaches. For the first time, contributions from both leading experts in the field and younger promising researchers are combined to give a comprehensive description of the recently proposed techniques and the engineering problems tackled using these techniques. The book begins with a detailed introduction to the theories on which different multiscale approaches are based, with regards to linear Homogenisation as well as various nonlinear approa.

Solids --- Solid state physics. --- Mechanics. --- Multiscale modeling. --- Multi-scale modeling --- Multiscale models --- Mathematical models --- Multivariate analysis --- Classical mechanics --- Newtonian mechanics --- Physics --- Dynamics --- Quantum theory --- Solid state physics --- Transparent solids --- Mathematical models. --- Mechanics --- Multiscale modeling --- Solids - Mathematical models

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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.

Engineering. --- Numerical and Computational Methods in Engineering. --- Continuum Mechanics and Mechanics of Materials. --- Calculus of Variations and Optimal Control; Optimization. --- Vibration, Dynamical Systems, Control. --- Operations Research, Mathematical Programming. --- Mathematical optimization. --- Operations research. --- Materials. --- Vibration. --- Ingénierie --- Optimisation mathématique --- Recherche opérationnelle --- Matériaux --- Vibration --- Mathematics. --- Mechanics -- Mathematical models. --- Solids -- Mathematical models. --- Engineering & Applied Sciences --- Computer Science --- Mechanics --- Solids --- Mathematical models. --- Classical mechanics --- Newtonian mechanics --- Calculus of variations. --- Management science. --- Computational intelligence. --- Continuum mechanics. --- Dynamical systems. --- Dynamics. --- Computational Intelligence. --- Operations Research, Management Science. --- Dynamical systems --- Kinetics --- Mathematics --- Mechanics, Analytic --- Force and energy --- Physics --- Statics --- Cycles --- Sound --- Mechanics of continua --- Elasticity --- Field theory (Physics) --- Intelligence, Computational --- Artificial intelligence --- Soft computing --- Quantitative business analysis --- Management --- Problem solving --- Operations research --- Statistical decision --- Operational analysis --- Operational research --- Industrial engineering --- Management science --- Research --- System theory --- Isoperimetrical problems --- Variations, Calculus of --- Maxima and minima --- Construction --- Industrial arts --- Technology --- Solid state physics --- Transparent solids --- Dynamics --- Quantum theory --- Mechanics. --- Mechanics, Applied. --- Solid Mechanics. --- Optimization (Mathematics) --- Optimization techniques --- Optimization theory --- Systems optimization --- Mathematical analysis --- Simulation methods --- System analysis --- Applied mechanics --- Engineering, Mechanical --- Engineering mathematics