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Rate-Independent Systems

Theory and Application

  • Alexander Mielke
  • Tomáš Roubíček

Part of the Applied Mathematical Sciences book series (AMS, volume 193)

Table of contents

  1. Front Matter
    Pages i-xxii
  2. Alexander Mielke, Tomàš Roubíček
    Pages 1-43
  3. Alexander Mielke, Tomàš Roubíček
    Pages 45-115
  4. Alexander Mielke, Tomàš Roubíček
    Pages 117-234
  5. Alexander Mielke, Tomàš Roubíček
    Pages 235-458
  6. Alexander Mielke, Tomàš Roubíček
    Pages 459-577
  7. Back Matter
    Pages 579-660

About this book

Introduction

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.

Keywords

computational mechanics contact mechanics continuum mechanics of solids damage dissipation potentials energetic solutions energy functionals evolutionary gamma convergence inelastic processes mutual recovery sequences numerical methods for rate-independent systems partial differential inequalities phase transformations plasticity rate-independent evolutionary systems thermodynamics weak solutions

Authors and affiliations

  • Alexander Mielke
    • 1
  • Tomáš Roubíček
    • 2
  1. 1.Weierstraß-Institut fürAngewandte Analysis und StochastikBerlinGermany
  2. 2.Charles UniversityMathematical InstitutePragueCzech Republic

Bibliographic information

  • DOI https://doi.org/10.1007/978-1-4939-2706-7
  • Copyright Information Springer Science+Business Media New York 2015
  • Publisher Name Springer, New York, NY
  • eBook Packages Mathematics and Statistics
  • Print ISBN 978-1-4939-2705-0
  • Online ISBN 978-1-4939-2706-7
  • Series Print ISSN 0066-5452
  • Series Online ISSN 2196-968X
  • Buy this book on publisher's site