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This book addresses the need for a fundamental understanding of the physical origin, the mathematical behavior and the numerical treatment of models which include microstructure. Leading scientists present their efforts involving mathematical analysis, numerical analysis, computational mechanics, material modelling and experiment. The mathematical analyses are based on methods from the calculus of variations, while in the numerical implementation global optimization algorithms play a central role. The modeling covers all length scales, from the atomic structure up to macroscopic samples. The development of the models ware guided by experiments on single and polycrystals and results will be checked against experimental data.

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Numerical algorithms for the simulation of finite plasticity with microstructures.- Analytical and numerical aspects of relaxation and regularization in models of crystal plasticity.- Modeling and computation of time-continuous evolution of - Hybrid micro-macro modeling of evolving microstructures in finite plasticity.-Regularizations and relaxations of time-continuous problems in plasticity.- Discrete and phase field models of dislocations and their macroscopic limits.- Experimental analysis of the orientation dependence of deformation laminates.- Statistically similar representative microstructures in elasto-plasticity.

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