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
59/2004

Scaling of the energy for thin martensitic films

Nirmalendu Chaudhuri and Stefan Müller

Abstract

We study the scaling behaviour of thin martensitic films. Specifically we consider an elastic energy with two SO(3) invariant wells which are strongly incompatible in the sense of Matos and Šverák, but whose two-dimensional projections are compatible. We show that in a thin film of thickness the energy per unit height scales like $h$. This scaling lies in between the classical membrane theory (where the energy per unit height is of order 1) and the Kirchhoff bending theory, which corresponds to a scaling of $h^2$.

Received:
Sep 20, 2004
Published:
Sep 20, 2004
MSC Codes:
74K20, 74N10, 74B20
Keywords:
martensitic films, phase transformation

Related publications

inJournal
2006 Repository Open Access
Nirmalendu Chaudhuri and Stefan Müller

Scaling of the energy for thin martensitic films

In: SIAM journal on mathematical analysis, 38 (2006) 2, pp. 468-477