Optimization of the branching pattern in coherent phase transitions

Patrick Dondl; Behrend Heeren; Martin Rumpf

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arXiv · 1512.06620

Optimization of the branching pattern in coherent phase transitions

Patrick Dondl·Behrend Heeren·Martin Rumpf

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Abstract

Branching can be observed at the austenite-martensite interface of martensitic phase transformations. For a model problem, Kohn and M\"uller studied a branching pattern with optimal scaling of the energy with respect to its parameters. Here, we present finite element simulations that suggest a topologically different class of branching patterns and derive a novel, low dimensional family of patterns. After a geometric optimization within this family, the resulting pattern bears a striking resemblance to our simulation. The novel microstructure admits the same scaling exponents but results in a significantly lower upper energy bound.

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Patrick Dondl, Behrend Heeren, Martin Rumpf. 2015-12-21. Optimization of the branching pattern in coherent phase transitions. https://arxiv.org/abs/1512.06620

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