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Quasiconvexity at the boundary and the nucleation of austenite

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posted on 2023-06-09, 04:54 authored by J M Ball, Konstantinos KoumatosKonstantinos Koumatos
Motivated by experimental observations of H. Seiner et al., we study the nucleation of austenite in a single crystal of a CuAlNi shape-memory alloy stabilized as a single variant of martensite. In the experiments the nucleation process was induced by localized heating and it was observed that, regardless of where the localized heating was applied, the nucleation points were always located at one of the corners of the sample - a rectangular parallelepiped in the austenite. Using a simplified nonlinear elasticity model, we propose an explanation for the location of the nucleation points by showing that the martensite is a local minimizer of the energy with respect to localized variations in the interior, on faces and edges of the sample, but not at some corners, where a localized microstructure, involving austenite and a simple laminate of martensite, can lower the energy. The result for the interior, faces and edges is established by showing that the free-energy function satisfies a set of quasiconvexity conditions at the stabilized variant in the interior, faces and edges, respectively, provided the specimen is suitably cut.

History

Publication status

  • Published

File Version

  • Accepted version

Journal

Archive for Rational Mechanics and Analysis

ISSN

0003-9527

Publisher

Springer Verlag

Issue

1

Volume

219

Page range

89-157

Department affiliated with

  • Mathematics Publications

Research groups affiliated with

  • Analysis and Partial Differential Equations Research Group Publications

Full text available

  • Yes

Peer reviewed?

  • Yes

Legacy Posted Date

2017-01-24

First Open Access (FOA) Date

2017-01-24

First Compliant Deposit (FCD) Date

2017-01-24

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