Damage as the Γ-limit of microfractures in linearized elasticity under the non-interpenetration constraint

Scardia, L. (2010) Damage as the Γ-limit of microfractures in linearized elasticity under the non-interpenetration constraint. Advances in Calculus of Variations, 3(4), pp. 423-458. (doi: 10.1515/acv.2010.020)

Abstract

A homogenization result is given for a material with brittle periodic inclusions, under the requirement that the interpenetration of matter is forbidden. According to the ratio between the softness of the inclusions and the size of the microstucture, three different limit models are deduced via Gamma-convergence. In particular it is shown that in the limit the non-interpenetration constraint breaks the symmetry between states where the material is in extension and in compression.

• Item Type: Articles
• Status: Published
• Refereed: Yes
• Glasgow Author(s) Enlighten ID: Scardia, Dr Lucia
• Authors: Scardia, L.
• Subjects: Q Science > QA Mathematics
• College/School: College of Science and Engineering > School of Mathematics and Statistics > Mathematics
• Journal Name: Advances in Calculus of Variations
• Journal Abbr.: Adv. Calc. Var.
• Publisher: Walter de Gruyter
• ISSN: 1864-8258
• ISSN (Online): 1864-8266
• Published Online: 20 October 2010
• Copyright Holders: Copyright © 2010 Walter de Gruyter
• First Published: First published in Advances in Calculus of Variations 3(4):423-458
• Publisher Policy: Reproduced in accordance with the copyright policy of the publisher