Line-tension model for plasticity as the Γ-limit of a nonlinear dislocation energy

L. Scardia, C.I. Zeppieri

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20 Citations (Scopus)
27 Downloads (Pure)

Abstract

In this paper we rigorously derive a line-tension model for plasticity as the G-limit of a nonlinear mesoscopic dislocation energy, without resorting to the introduction of an ad hoc cut-off radius. The G-limit we obtain as the length of the Burgers vector tends to zero has the same form as the G-limit obtained by starting from a linear, semidiscrete dislocation energy. The nonlinearity, however, creates several mathematical difficulties, which we tackled by proving suitable versions of the rigidity estimate in non-simply-connected domains and by performing a rigorous two-scale linearization of the energy around an equilibrium configuration.
Original languageEnglish
Pages (from-to)2372-2400
JournalSIAM Journal on Mathematical Analysis
Volume44
Issue number4
DOIs
Publication statusPublished - 2012

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Burgers vector
Dislocation
Plasticity
Rigidity
Line
Energy
Model
Nonlinearity
Tend
Configuration
Zero
Estimate

Cite this

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abstract = "In this paper we rigorously derive a line-tension model for plasticity as the G-limit of a nonlinear mesoscopic dislocation energy, without resorting to the introduction of an ad hoc cut-off radius. The G-limit we obtain as the length of the Burgers vector tends to zero has the same form as the G-limit obtained by starting from a linear, semidiscrete dislocation energy. The nonlinearity, however, creates several mathematical difficulties, which we tackled by proving suitable versions of the rigidity estimate in non-simply-connected domains and by performing a rigorous two-scale linearization of the energy around an equilibrium configuration.",
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Line-tension model for plasticity as the Γ-limit of a nonlinear dislocation energy. / Scardia, L.; Zeppieri, C.I.

In: SIAM Journal on Mathematical Analysis, Vol. 44, No. 4, 2012, p. 2372-2400.

Research output: Contribution to journalArticleAcademicpeer-review

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AU - Scardia, L.

AU - Zeppieri, C.I.

PY - 2012

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AB - In this paper we rigorously derive a line-tension model for plasticity as the G-limit of a nonlinear mesoscopic dislocation energy, without resorting to the introduction of an ad hoc cut-off radius. The G-limit we obtain as the length of the Burgers vector tends to zero has the same form as the G-limit obtained by starting from a linear, semidiscrete dislocation energy. The nonlinearity, however, creates several mathematical difficulties, which we tackled by proving suitable versions of the rigidity estimate in non-simply-connected domains and by performing a rigorous two-scale linearization of the energy around an equilibrium configuration.

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JO - SIAM Journal on Mathematical Analysis

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