Optimization of the branching pattern in coherent phase transitions
For researchers studying coherent phase transitions, this work provides a more energetically favorable microstructure, improving upon the classical Kohn-Müller model.
The paper identifies a new class of branching patterns in martensitic phase transformations that yields a significantly lower upper energy bound than previously known patterns, while maintaining the same scaling exponents.
Branching can be observed at the austenite-martensite interface of martensitic phase transformations. For a model problem, Kohn and Müller 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.