Young measure flow as a model for damage

Marc Oliver Rieger; J Zimmer

doi:10.1007/s00033-008-7016-3

Young measure flow as a model for damage

Marc Oliver Rieger, J Zimmer

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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.

Original language	English
Pages (from-to)	1-32
Number of pages	32
Journal	Zeitschrift für Angewandte Mathematik und Physik
Volume	60
Issue number	1
Early online date	5 Jul 2008
DOIs	https://doi.org/10.1007/s00033-008-7016-3
Publication status	Published - Jan 2009

Keywords

Fracture
Elasticity
Continuum mechanics

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10.1007/s00033-008-7016-3

riegerzimmer
The final publication is available at Springer via http://dx.doi.org/10.1007/s00033-008-7016-3
Submitted manuscript, 344 KB

Cite this

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Young measure flow as a model for damage

Abstract

Keywords

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MATHEMATICAL ANALYSIS OF THE STATIC AND DYNAMIC BEHAVIOUR OF MATERIALS WITH PHASE TRANSITIONS AND MICROSTRUCTURES

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Young measure flow as a model for damage

Abstract

Keywords

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MATHEMATICAL ANALYSIS OF THE STATIC AND DYNAMIC BEHAVIOUR OF MATERIALS WITH PHASE TRANSITIONS AND MICROSTRUCTURES

Cite this