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arXiv · 2210.04304

On Rigidity for the Four-Well Problem Arising in the Cubic-to-Trigonal Phase Transformation

Angkana Rüland·Theresa M. Simon
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Abstract

We classify all exactly stress-free solutions to the cubic-to-trigonal phase transformation within the geometrically linearized theory of elasticity, showing that only simple laminates and crossing-twin structures can occur. In particular, we prove that although this transformation is closely related to the cubic-to-orthorhombic phase transformation, all its solutions are rigid. The argument relies on a combination of the Saint-Venant compatibility conditions together with the underlying nonlinear relations and non-convexity conditions satisfied by the strain components.

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Angkana Rüland, Theresa M. Simon. 2022-10-09. On Rigidity for the Four-Well Problem Arising in the Cubic-to-Trigonal Phase Transformation. https://arxiv.org/abs/2210.04304

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