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Upscaling of dislocation walls in finite domains
Eindhoven University of Technology, Netherlands.
Eindhoven University of Technology, Netherlands .ORCID iD: 0000-0002-1160-0007
Eindhoven University of Technology, Netherlands.
2014 (English)In: European journal of applied mathematics (Print), ISSN 0956-7925, E-ISSN 1469-4425, Vol. 25, no 6, p. 749-781Article in journal (Refereed) Published
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Abstract [en]

We wish to understand the macroscopic plastic behaviour of metals by upscaling the micromechanics of dislocations. We consider a highly simplified dislocation network, which allows our discrete model to be a one dimensional particle system, in which the interactions between the particles (dislocation walls) are singular and non-local. As a first step towards treating realistic geometries, we focus on finite-size effects rather than considering an infinite domain as typically discussed in the literature. We derive effective equations for the dislocation density by means of Gamma-convergence on the space of probability measures. Our analysis yields a classification of macroscopic models, in which the size of the domain plays a key role.

Place, publisher, year, edition, pages
New York: Cambridge University Press, 2014. Vol. 25, no 6, p. 749-781
Keywords [en]
: Plasticity; Multiscale; Straight edge-dislocations; Discrete-to-continuum limit; Γ- convergence; 74Q05, 74C05, 82B21, 49J45, 82D35
National Category
Materials Engineering Mathematical Analysis
Research subject
Mathematics; Mechanical Engineering
Identifiers
URN: urn:nbn:se:kau:diva-39777DOI: 10.1017/S0956792514000254ISI: 000344494600004Scopus ID: 2-s2.0-84906529121OAI: oai:DiVA.org:kau-39777DiVA, id: diva2:901176
Available from: 2016-02-06 Created: 2016-02-06 Last updated: 2017-11-30Bibliographically approved

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Muntean, Adrian

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