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

Scardia, L. and Zeppieri, C. (2012) Line-tension model for plasticity as the Gamma-limit of a nonlinear dislocation energy. SIAM: Journal on Mathematical Analysis, 44(4), pp. 2372-2400. (doi: 10.1137/110824851)

Abstract

In this paper we rigorously derive a line-tension model for plasticity as the Gamma-limit of a nonlinear mesoscopic dislocation energy, without resorting to the introduction of an ad hoc cut-off radius. The Gamma-limit we obtain as the length of the Burgers vector tends to zero has the same form as the Gamma-limit obtained by starting from a linear, semi-discrete 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 linearisation of the energy around an equilibrium configuration.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Scardia, Dr Lucia
• Authors: Scardia, L., and Zeppieri, C.
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: SIAM: Journal on Mathematical Analysis
• Publisher: Society for Industrial and Applied Mathematics
• ISSN: 0036-1410
• ISSN (Online): 1095-7154
• Copyright Holders: Copyright © 2012 Society for Industrial and Applied Mathematics
• First Published: First published in SIAM Journal on Mathematical Analysis
• Publisher Policy: Reproduced in accordance with the copyright policy of the publisher