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Relaxation of rate-independent evolution problems

Published online by Cambridge University Press:  12 July 2007

Florian Theil
Affiliation:
University of Warwick, Mathematics Institute, Coventry CV4 7AL, UK (theil@maths.warwick.ac.uk)

Abstract

The relaxation of certain time-evolution problems is investigated. As a conceptually simple example, we study elastically deformable bodies that undergo martensitic phase transformations. The movement of the phase boundaries is hindered by dry friction. The fundamental problem is that the phase distribution forms a highly oscillatory microstructure in space. Therefore, it is desirable to derive a coarse-grained system that describes the effective properties. We introduce a concept of relaxation of the evolution system and apply it to the case where only two phases occur and the elastic energy is quadratic. Finally, we present a candidate for the relaxation in the general case.

Type
Research Article
Copyright
Copyright © Royal Society of Edinburgh 2002

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