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Rate-independent systemstheory and a...

Mielke, Alexander.

Rate-independent systemstheory and application /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Rate-independent systemsby Alexander Mielke, Tomas Roubicek.
Reminder of title:	theory and application /
Author:	Mielke, Alexander.
other author:	Roubicek, Tomas.
Published:	New York, NY :Springer New York :2015.
Description:	xxii, 660 p. :ill., digital ;24 cm.
Contained By:	Springer eBooks
Subject:	Differential equations, Partial.
Online resource:	http://dx.doi.org/10.1007/978-1-4939-2706-7
ISBN:	9781493927067$q(electronic bk.)

Rate-independent systemstheory and application /
Mielke, Alexander.

Rate-independent systemstheory and application /[electronic resource] :by Alexander Mielke, Tomas Roubicek. - New York, NY :Springer New York :2015. - xxii, 660 p. :ill., digital ;24 cm. - Applied mathematical sciences,v.1930066-5452 ;. - Applied mathematical sciences ;v.176..

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.

ISBN: 9781493927067$q(electronic bk.)

Standard No.: 10.1007/978-1-4939-2706-7doiSubjects--Topical Terms:

189753
Differential equations, Partial.

LC Class. No.: QA377

Dewey Class. No.: 515.353

Rate-independent systemstheory and application /
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520 $a 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.
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