From discrete visco-elasticity to continuum rate-independent plasticity : rigorous results
dc.bibliographicCitation.volume | 1541 | |
dc.contributor.author | Mielke, Alexander | |
dc.contributor.author | Truskinovsky, Lev | |
dc.date.accessioned | 2016-03-24T17:38:38Z | |
dc.date.available | 2019-06-28T08:05:39Z | |
dc.date.issued | 2010 | |
dc.description.abstract | We 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. | eng |
dc.description.version | publishedVersion | eng |
dc.format | application/pdf | |
dc.identifier.issn | 0946-8633 | |
dc.identifier.uri | https://doi.org/10.34657/2413 | |
dc.identifier.uri | https://oa.tib.eu/renate/handle/123456789/2330 | |
dc.language.iso | eng | eng |
dc.publisher | Berlin : Weierstraß-Institut für Angewandte Analysis und Stochastik | eng |
dc.relation.ispartofseries | Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik, Volume 1541, ISSN 0946-8633 | eng |
dc.rights.license | This document may be downloaded, read, stored and printed for your own use within the limits of § 53 UrhG but it may not be distributed via the internet or passed on to external parties. | eng |
dc.rights.license | Dieses Dokument darf im Rahmen von § 53 UrhG zum eigenen Gebrauch kostenfrei heruntergeladen, gelesen, gespeichert und ausgedruckt, aber nicht im Internet bereitgestellt oder an Außenstehende weitergegeben werden. | ger |
dc.subject | Snap-spring potential | eng |
dc.subject | hysteresis | eng |
dc.subject | Gamma convergence for evolution | eng |
dc.subject | rate-independent plasticity | eng |
dc.subject | viscous gradient flow | eng |
dc.subject | wiggly energy | eng |
dc.subject.ddc | 510 | eng |
dc.title | From discrete visco-elasticity to continuum rate-independent plasticity : rigorous results | eng |
dc.type | report | eng |
dc.type | Text | eng |
dcterms.bibliographicCitation.journalTitle | Preprint / Weierstraß-Institut für Angewandte Analysis und Stochastik | eng |
tib.accessRights | openAccess | eng |
wgl.contributor | WIAS | eng |
wgl.subject | Mathematik | eng |
wgl.type | Report / Forschungsbericht / Arbeitspapier | eng |
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