English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

We study a simplified two-dimensional model for a cubic-to-orthorhombic phasetransition occuring in certain shape-memory-alloys. In the low temperatureregime the linear theory of elasticity predicts various possible patterns ofmartensite arrangements: Apart from the well known laminates this phasetransition displays additional structures involving four martensitic variants-- so called crossing twins. Introducing a variational model including surfaceenergy, we show that these structures are rigid under small energyperturbations. Combined with an upper bound construction this gives the optimalscaling behavior of incompatible microstructures. These results are related topapers by Capella and Otto as well as to a paper by Dolzmann and M\"uller.

A Rigidity Result for a Reduced Model of a Cubic-to-Orthorhombic Phase Transition in the Geometrically Linear Theory of Elasticity