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Advances in Calculus of Variations

Managing Editor: Duzaar, Frank / Kinnunen, Juha

Editorial Board: Armstrong, Scott N. / Balogh, Zoltán / Cardiliaguet, Pierre / Dacorogna, Bernard / Dal Maso, Gianni / DiBenedetto, Emmanuele / Fonseca, Irene / Gianazza, Ugo / Ishii, Hitoshi / Kristensen, Jan / Manfredi, Juan / Martell, Jose Maria / Mingione, Giuseppe / Nystrom, Kaj / Riviére, Tristan / Schaetzle, Reiner / Shen, Zhongwei / Silvestre, Luis / Tonegawa, Yoshihiro / Touzi, Nizar / Wang, Guofang

IMPACT FACTOR 2018: 2.316

CiteScore 2018: 1.77

SCImago Journal Rank (SJR) 2018: 2.350
Source Normalized Impact per Paper (SNIP) 2018: 1.465

Mathematical Citation Quotient (MCQ) 2018: 1.44

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Volume 6, Issue 2


Fracture and plastic models as Γ-limits of damage models under different regimes

Flaviana Iurlano
Published Online: 2013-04-01 | DOI: https://doi.org/10.1515/acv-2011-0011


We consider a variational model for damaged elastic materials. This model depends on three small parameters, which are related to the cost of the damage, to the width of the damaged regions, and to the minimum elasticity constant attained in the damaged regions. As these parameters tend to zero, our models Γ-converge to a model for brittle fracture, for fracture with a cohesive zone, or for perfect plasticity, depending on the asymptotic ratios of the three parameters.

Keywords: Damage problems; fracture mechanics; cohesive zone models; Hencky's plasticity model; Γ-convergence

About the article

Received: 2011-11-01

Revised: 2012-03-12

Accepted: 2012-04-12

Published Online: 2013-04-01

Published in Print: 2013-04-01

Citation Information: Advances in Calculus of Variations, Volume 6, Issue 2, Pages 165–189, ISSN (Online) 1864-8266, ISSN (Print) 1864-8258, DOI: https://doi.org/10.1515/acv-2011-0011.

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