Rate-Independent Systems

This monograph provides both an introduction to and a thorough exposition of the theory of rate-independent systems, which the authors have been working on with a lot of collaborators over 15 years. The focus is mostly on fully rate-independent systems, first on an abstract level either with or even without a linear structure, discussing various concepts of solutions with full mathematical rigor. Then, usefulness of the abstract concepts is 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. A few other physical systems, e.g. magnetic or ferroelectric materials, and couplings to rate-dependent thermodynamic models are considered as well. Selected applications are accompaniedby numerical simulations illustrating both the models and the efficiency of computational algorithms.

In this book, the mathematical framework for a rigorous mathematical treatment of "rate-independent systems" is presented 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.

The mathematical framework for a rigorous mathematical treatment of rate-independent systems, together with various applications, is presented in a comprehensive form for the first time. Provides existence theorems and tools for discussing numerical solutions. Key international researchers in this field Motivates mathematical theory for scientists by use of examples Includes supplementary material: sn.pub/extras

Auteur

Alexander Mielke is Professor at Humboldt University of Berlin as well as a head of the research group "Partial Differential Equations" at the Weierstrass Institute for Applied Analysis and Stochastics. His research interest range over applied mathematical analysis, partial differential equations, multi-scale modeling and applications in continuum physics.

Tomá Roubíek is a Professor at Charles University in Prague, as well as a researcher at Institute of Thermomechanics and also at Institute of Information Theory and Automation of the Czech Academy of Sciences. Having an engineering background, his professional activity has evolved from computer simulations of systems of nonlinear partial differential equations thru numerical mathematics and optimization theory to applied mathematical analysis focused to mathematical modeling in engineering and physics.

Contenu

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.