Rate-Independent Systems : Theory and Application

0509076 - ÚTIA 2020 RIV US eng B - Monografie kniha jako celek
Mielke, A. - Roubíček, Tomáš
Rate-Independent Systems : Theory and Application.
New York: Springer, 2015. 660 s. Applied Mathematical Sciences-Series, 193. ISBN 978-1-4939-2705-0. ISSN 0066-5452
Grant CEP: GA ČR GA201/09/0917; GA ČR GAP201/10/0357; GA ČR GA13-18652S; GA ČR GA14-15264S
Institucionální podpora: RVO:67985556
Klíčová slova: computational mechanics * contact mechanics * continuum mechanics of solids * damage * dissipation potentials * energetic solutions * energy functionals
Obor OECD: Pure mathematics
http://library.utia.cas.cz/separaty/2019/MTR/roubicek-0509076.pdf

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.
Trvalý link: http://hdl.handle.net/11104/0299870