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

Angkana Rüland

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Submission date: 03. May. 2013
Pages: 63
published in: Archive for rational mechanics and analysis, 221 (2016) 1, p. 23-106 
DOI number (of the published article): 10.1007/s00205-016-0971-5
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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 linearized 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 values of δ.