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

Rüland, A.; Simon, T.M.

Forschungsartikel (Zeitschrift) | Peer reviewed

Zusammenfassung

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.

Details zur Publikation

FachzeitschriftJournal of Elasticity
Jahrgang / Bandnr. / Volume153
Seitenbereich455-475
StatusVeröffentlicht
Veröffentlichungsjahr2023
Sprache, in der die Publikation verfasst istEnglisch
DOI10.1007/s10659-023-10011-2
Stichwörtershape-memory alloy; rigidity; structure result; cubic-to-trigonal phase transformation; geometrically linearized theory

Autor*innen der Universität Münster

Simon, Theresa
Juniorprofessur für Angewandte Mathematik (Prof. Simon)