Analysis of a Moving Mask Hypothesis for Martensitic Transformations

  • Francesco Della PortaEmail author


In this work we introduce a moving mask hypothesis to describe the dynamics of austenite-to-martensite phase transitions at a continuum level. In this framework, we prove a new type of Hadamard jump condition, from which we deduce that the deformation gradient \(\nabla \mathbf {y}\) must satisfy the differential constraint \({{\,\mathrm{\mathsf {cof}}\,}}(\nabla \mathbf {y} -\mathsf {1}) = \mathsf {0}\) a.e. in the martensite phase. This provides a selection mechanism for physically relevant energy-minimizing microstructures and is useful to better understand the complex microstructures and the formation of curved interfaces between phases in new ultra-low hysteresis alloys such as Zn45Au30Cu25. In particular, we use the new type of Hadamard jump condition to deduce a rigidity theorem for the two-well problem. The latter provides more insight on the cofactor conditions, particular conditions of supercompatibility between phases believed to influence reversibility of martensitic transformations.


Martensitic phase transitions Selection mechanism Microstructures Moving mask Cofactor conditions 

Mathematics Subject Classification

74A50 74N05 74N10 74N15 74N20 



This work was supported by the Engineering and Physical Sciences Research Council [EP/L015811/1]. The author would like to thank John Ball for his helpful suggestions and feedback which greatly improved this work, as well as Richard James, Giacomo Canevari and Xian Chen for the useful discussions. The author would like to acknowledge the two anonymous referees for carefully reading this paper and improving it with their comments.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.


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Authors and Affiliations

  1. 1.Mathematical InstituteUniversity of OxfordOxfordUK
  2. 2.Max-Planck Institute for Mathematics in the SciencesLeipzigGermany

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