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The Cubic-to-Orthorhombic Phase Transition: Rigidity and Non-Rigidity Properties in the Linear Theory of Elasticity

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Abstract

In this paper we investigate the cubic-to-orthorhombic phase transition in the framework of linear elasticity. Using convex integration techniques, we prove that this phase transition represents one of the simplest three-dimensional examples in which already the linearised theory of elasticity displays non-rigidity properties. As a complementary result, we demonstrate that surface energy constraints rule out such highly oscillatory behaviour. We give a full characterization of all possibly emerging patterns for generic material parameters.

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  1. Angkana Rüland

    Present address: Mathematical Institute, University of Oxford, Andrew Wiles Building, Oxford, OX2 6GG, UK

Authors and Affiliations

  1. Mathematisches Institut, Universität Bonn, Endenicher Allee 60, 53115, Bonn, Germany

    Angkana Rüland

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  1. Angkana Rüland
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Correspondence to Angkana Rüland.

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Communicated by V. Šverák

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Rüland, A. The Cubic-to-Orthorhombic Phase Transition: Rigidity and Non-Rigidity Properties in the Linear Theory of Elasticity. Arch Rational Mech Anal 221, 23–106 (2016). https://doi.org/10.1007/s00205-016-0971-5

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  • DOI: https://doi.org/10.1007/s00205-016-0971-5

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