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＜電子ブック＞
Rate-Independent Systems : Theory and Application / by Alexander Mielke, Tomáš Roubíček
(Applied Mathematical Sciences. ISSN:2196968X ; 655)

版	1st ed. 2015.
出版者	(New York, NY : Springer New York : Imprint: Springer)
出版年	2015
大きさ	XXII, 660 p. 75 illus., 13 illus. in color : online resource
著者標目	*Mielke, Alexander author Roubíček, Tomáš author SpringerLink (Online service)
件　名	LCSH:Differential equations LCSH:Mathematical physics LCSH:Mechanics, Applied LCSH:Solids FREE:Differential Equations FREE:Mathematical Methods in Physics FREE:Solid Mechanics
一般注記	1. A general view on rate-independent systems -- 2. Energetic rate-independent systems -- 3. Rate-independent systems in Banach spaces -- 4. Applications in continuum mechanics and physics of solids -- 5. Beyond rate independence -- Appendices -- References -- Index This monograph provides both an introduction to and a thorough exposition of the theory of rate-independent systems, which the authors have worked on with a number of collaborators over many years. The focus is mostly on fully rate-independent systems, first on an abstract level with or without a linear structure, discussing various concepts of solutions with full mathematical rigor. The usefulness of the abstract concepts is then demonstrated on the level of various applications primarily in continuum mechanics of solids, including suitable approximation strategies with guaranteed numerical stability and convergence. Particular applications concern inelastic processes such as plasticity, damage, phase transformations, or adhesive-type contacts both at small strains and at finite strains. Other physical systems such as magnetic or ferroelectric materials, and couplings to rate-dependent thermodynamic models are also considered. Selected applications are accompanied by numerical simulations illustrating both the models and the efficiency of computational algorithms. This book presents the mathematical framework for a rigorous mathematical treatment of rate-independent systems in a comprehensive form for the first time. Researchers and graduate students in applied mathematics, engineering, and computational physics will find this timely and well-written book useful HTTP:URL=https://doi.org/10.1007/978-1-4939-2706-7

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