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A proof of Taylor scaling for curvature-driven dislocation motion through random arrays of obstacles

Courte, Luca and Dondl, Patrick and Ortiz, Michael (2021) A proof of Taylor scaling for curvature-driven dislocation motion through random arrays of obstacles. . (Unpublished)

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We prove Taylor scaling for dislocation lines characterized by line-tension and moving by curvature under the action of an applied shear stress in a plane containing a random array of obstacles. Specifically, we show--in the sense of optimal scaling--that the critical applied shear stress for yielding, or percolation-like unbounded motion of the dislocation, scales in proportion to the square root of the obstacle density. For sufficiently small obstacle densities, Taylor scaling dominates the linear-scaling that results from purely energetic considerations and, therefore, characterizes the dominant rate-limiting mechanism in that regime.

Item Type:Report or Paper (Discussion Paper)
Related URLs:
URLURL TypeDescription Paper
Dondl, Patrick0000-0003-3035-7230
Ortiz, Michael0000-0001-5877-4824
Additional Information:LC acknowledges support from the Fonds National de la Recherche, Luxembourg (AFR Grant 13502370). PWD gratefully acknowledges partial support from the Deutsche Forschungsgemeinschaft (Grant No. Do 1412/4-1 within SPP 2265). MO gratefully acknowledges support from the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) via project 211504053 - SFB 1060 and project 390685813 - GZ 2047/1 - HCM.
Funding AgencyGrant Number
Fonds National de la Recherche (Luxembourg)13502370
Deutsche Forschungsgemeinschaft (DFG)1412/4-1 - SPP 2265
Deutsche Forschungsgemeinschaft (DFG)211504053 - SFB 1060
Deutsche Forschungsgemeinschaft (DFG)390685813 - GZ 2047/1
Subject Keywords:Dislocations, random media, Taylor scaling, flow stress, curvature flow, differential inclusions, dry friction, viscosity solutions
Classification Code:2010 Mathematics Subject Classification. 35R60, 35D40, 74A40, 74C99
Record Number:CaltechAUTHORS:20210719-210159826
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Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:109925
Deposited By: George Porter
Deposited On:19 Jul 2021 22:46
Last Modified:19 Jul 2021 22:46

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