Search

MiS Preprint Repository

We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

MiS Preprint
107/2013

Nucleation barriers at corners for cubic-to-tetragonal phase transformation

Peter Bella and Michael Goldman

Abstract

We are interested in the energetic cost of a martensitic inclusion of volume $V$ in austenite for the cubic-to-tetragonal phase transformation. In contrast with the work of [Knüpfer, Kohn, Otto: Comm. Pure Appl. Math. 66 (2013), no. 6, 867-904], we consider domain with a corner and obtain a better scaling law for the minimal energy ($E_{min} \sim \min(V^{2/3},V^{7/9})$). Our predictions are in a good agreement with physical experiments where nucleation of martensite is usually observed near the corners of the specimen.

Received:
Nov 22, 2013
Published:
Nov 26, 2013

Related publications

inJournal
2015 Repository Open Access
Peter Bella and Michael Goldman

Nucleation barriers at corners for cubic-to-tetragonal phase transformation

In: Proceedings of the Royal Society of Edinburgh / A, 145 (2015) 4, pp. 715-724