Browsing by Author "Truskinovsky, Lev"
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- ItemFrom discrete visco-elasticity to continuum rate-independent plasticity : rigorous results(Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik, 2010) Mielke, Alexander; Truskinovsky, LevWe show that continuum models for ideal plasticity can be obtained as a rigorous mathematical limit starting from a discrete microscopic model describing a visco-elastic crystal lattice with quenched disorder. The constitutive structure changes as a result of two concurrent limiting procedures: the vanishing-viscosity limit and the discrete to continuum limit. In the course of these limits a non-convex elastic problem transforms into a convex elastic problem while the quadratic rate-dependent dissipation of visco-elastic solid transforms into a singular rate-independent dissipation of an ideally plastic solid. In order to emphasize ideas we employ in our proofs the simplest prototypical system describing transformational plasticity of shape-memory alloys. The approach, however, is sufficiently general and can be used for similar reductions in the cases of more general plasticity and damage models.
- ItemMaterial Theories(Zürich : EMS Publ. House, 2017) DeSimone, Antonio; Luckhaus, Stephan; Truskinovsky, LevMaterial theories is a series of workshops concerned with a broad range of topics related to the mechanics and mathematics of materials. As such, this edition brought together researchers from diverse fields converging toward the interaction between mathematics, mechanics, and material science.
- ItemMaterial Theories(Zürich : EMS Publ. House, 2009) Luckhaus, Stephan; Truskinovsky, LevThis biennial workshop brings together mathematicians, mechanicians and theoretical physicists interested in developing new mathematical models of complex materials, medias and systems. The workshop covers a wide range of topics from nonequilibrium statistical mechanics and dynamical systems to calculus of variations and nonlinear functional analysis. A particular focus of this meeting was on continuum description of biological systems, pattern formation, granular media, plasticity and turbulence.
- ItemMaterial Theories(Zürich : EMS Publ. House, 2013) Luckhaus, Stephan; Truskinovsky, LevThe subject of this meeting was mathematical modeling of strongly interacting multi-particle systems that can be interpreted as advanced materials. The main emphasis was placed on contributions attempting to bridge the gap between discrete and continuum approaches, focusing on the multi-scale nature of physical phenomena and bringing new and nontrivial mathematics. The mathematical debates concentrated on nonlinear PDE, stochastic dynamical systems, optimal transportation, calculus of variations and large deviations theory.
- ItemMaterial Theories(Zürich : EMS Publ. House, 2007) Luckhaus, Stephan; Truskinovsky, LevThe workshop reviewed classical and recent trends in the modeling of material behavior using a wide spectrum of mathematical tools (stochastic processes, calculus of variations, pde’s). Among the topic covered, the following figured prominently: biology and biophysics, mechanics of nanostuctures, crystal plasticity, self-organized criticality, non equilibrium statistical mechanics, quantum mechanics, wetting phenomena, electronic transport in semiconductors, dislocation mechanics, kinetic theory, bucking in structural mechanics.
- ItemThermodynamische Materialtheorien(Zürich : EMS Publ. House, 2004) Müller, Ingo; Truskinovsky, LevThe meeting was focused on research in the broad field of thermodynamic constitutive theories. It provided a contact between physicists, engineers and mathematicians, whose talks led to lively and interesting discussions. The debate concentrated on the physical motivation of the models subjected to mathematical analysis.
- ItemThermodynamische Materialtheorien(Oberwolfach-Walke : Mathematisches Forschungsinstitut Oberwolfach, 2002) Müller, Ingo; Truskinovsky, Lev[no abstract available]