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Young measure flow as a model for damage


Rieger, Marc Oliver; Zimmer, Johannes (2009). Young measure flow as a model for damage. Zeitschrift für Angewandte Mathematik und Physik (ZAMP), 60(1):1-32.

Abstract

Models for hysteresis in continuum mechanics are studied that rely on a time-discretised quasi-static evolution of Young measures akin to a gradient flow. The main feature of this approach is that it allows for local, rather than global minimisation. In particular, the case of a non-coercive elastic energy density of Lennard-Jones type is investigated. The approach is used to describe the formation of damage in a material; existence results are proved, as well as several results highlighting the qualitative behaviour of solutions. Connections are made to recent variational models for fracture.

Abstract

Models for hysteresis in continuum mechanics are studied that rely on a time-discretised quasi-static evolution of Young measures akin to a gradient flow. The main feature of this approach is that it allows for local, rather than global minimisation. In particular, the case of a non-coercive elastic energy density of Lennard-Jones type is investigated. The approach is used to describe the formation of damage in a material; existence results are proved, as well as several results highlighting the qualitative behaviour of solutions. Connections are made to recent variational models for fracture.

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4 citations in Web of Science®
3 citations in Scopus®
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Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:03 Faculty of Economics > Department of Banking and Finance
Dewey Decimal Classification:330 Economics
Uncontrolled Keywords:Young measures - varifolds - damage - fracture - gradient flows
Language:English
Date:January 2009
Deposited On:05 Dec 2008 12:16
Last Modified:05 Apr 2016 12:38
Publisher:Birkhäuser
ISSN:0044-2275
Additional Information:The original publication is available at www.springerlink.com
Publisher DOI:https://doi.org/10.1007/s00033-008-7016-3

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