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The book presents the latest findings in experimental plasticity, crystal plasticity, phase transitions, advanced mathematical modeling of finite plasticity and multi-scale modeling. The associated algorithmic treatment is mainly based on finite element formulations for standard (local approach) as well as for non-standard (non-local approach) continua and for pure macroscopic as well as for directly coupled two-scale boundary value problems. Applications in the area of material design/processing are covered, ranging from grain boundary effects in polycrystals and phase transitions to deep-drawing of multiphase steels by directly taking into account random microstructures.

Microstructure. --- Plasticity. --- Engineering. --- Mathematical models. --- Continuum mechanics. --- Materials science. --- Continuum Mechanics and Mechanics of Materials. --- Mathematical Modeling and Industrial Mathematics. --- Characterization and Evaluation of Materials. --- Cohesion --- Deformations (Mechanics) --- Elasticity --- Plastics --- Rheology --- Materials --- Matter --- Morphology --- Micromechanics --- Stereology --- Constitution --- Mechanics. --- Mechanics, Applied. --- Surfaces (Physics). --- Solid Mechanics. --- Physics --- Surface chemistry --- Surfaces (Technology) --- Applied mechanics --- Engineering, Mechanical --- Engineering mathematics --- Classical mechanics --- Newtonian mechanics --- Dynamics --- Quantum theory --- Material science --- Physical sciences --- Models, Mathematical --- Simulation methods

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Generalized convexity conditions play a major role in many modern mechanical applications. They serve as the basis for existence proofs and allow for the design of advanced algorithms. Moreover, understanding these convexity conditions helps in deriving reliable mechanical models. The book summarizes the well established as well as the newest results in the field of poly-, quasi and rank-one convexity. Special emphasis is put on the construction of anisotropic polyconvex energy functions with applications to biomechanics and thin shells. In addition, phase transitions with interfacial energy and the relaxation of nematic elastomers are discussed.

Convex domains. --- Mechanics, Applied -- Mathematical models. --- Mechanics, Applied --- Convex domains --- Civil & Environmental Engineering --- Engineering & Applied Sciences --- Civil Engineering --- Mathematical models --- Mathematical models. --- Convex regions --- Convexity --- Engineering. --- Mechanics. --- Mechanics, Applied. --- Theoretical and Applied Mechanics. --- Calculus of variations --- Convex geometry --- Point set theory --- Mechanics, applied. --- Applied mechanics --- Engineering, Mechanical --- Engineering mathematics --- Classical mechanics --- Newtonian mechanics --- Physics --- Dynamics --- Quantum theory --- Rank-one convexity

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The book presents an overview of the state of research of advanced finite element technologies. Besides the mathematical analysis, the finite element development and their engineering applications are shown to the reader. The authors give a survey of the methods and technologies concerning efficiency, robustness and performance aspects. The book covers the topics of mathematical foundations for variational approaches and the mathematical understanding of the analytical requirements of modern finite element methods. Special attention is paid to finite deformations, adaptive strategies, incompressible, isotropic or anisotropic material behavior and the mathematical and numerical treatment of the well-known locking phenomenon. Beyond that new results for the introduced approaches are presented especially for challenging nonlinear problems.

Mathematics --- Classical mechanics. Field theory --- Applied physical engineering --- Engineering sciences. Technology --- Computer. Automation --- analyse (wiskunde) --- toegepaste wiskunde --- toegepaste mechanica --- computers --- economie --- informatica --- wiskunde --- ingenieurswetenschappen --- mechanica

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• Reference Manager
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The book presents the latest findings in experimental plasticity, crystal plasticity, phase transitions, advanced mathematical modeling of finite plasticity and multi-scale modeling. The associated algorithmic treatment is mainly based on finite element formulations for standard (local approach) as well as for non-standard (non-local approach) continua and for pure macroscopic as well as for directly coupled two-scale boundary value problems. Applications in the area of material design/processing are covered, ranging from grain boundary effects in polycrystals and phase transitions to deep-drawing of multiphase steels by directly taking into account random microstructures [SUDOC]