### Abstract

Original language | English |
---|---|

Pages (from-to) | 2372-2400 |

Journal | SIAM Journal on Mathematical Analysis |

Volume | 44 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2012 |

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*SIAM Journal on Mathematical Analysis*,

*44*(4), 2372-2400. https://doi.org/10.1137/110824851

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*SIAM Journal on Mathematical Analysis*, vol. 44, no. 4, pp. 2372-2400. https://doi.org/10.1137/110824851

**Line-tension model for plasticity as the Γ-limit of a nonlinear dislocation energy.** / Scardia, L.; Zeppieri, C.I.

Research output: Contribution to journal › Article › Academic › peer-review

TY - JOUR

T1 - Line-tension model for plasticity as the Γ-limit of a nonlinear dislocation energy

AU - Scardia, L.

AU - Zeppieri, C.I.

PY - 2012

Y1 - 2012

N2 - 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.

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.

U2 - 10.1137/110824851

DO - 10.1137/110824851

M3 - Article

VL - 44

SP - 2372

EP - 2400

JO - SIAM Journal on Mathematical Analysis

JF - SIAM Journal on Mathematical Analysis

SN - 0036-1410

IS - 4

ER -