# Phase Field Models for Thin Elastic Structures with Topological Constraint

@article{Dondl2015PhaseFM,
title={Phase Field Models for Thin Elastic Structures with Topological Constraint},
author={P. Dondl and A. Lemenant and Stephan Wojtowytsch},
journal={Archive for Rational Mechanics and Analysis},
year={2015},
volume={223},
pages={693-736}
}
• Published 2015
• Mathematics, Physics
• Archive for Rational Mechanics and Analysis
This article is concerned with the problem of minimising the Willmore energy in the class of connected surfaces with prescribed area which are confined to a small container. We propose a phase field approximation based on De Giorgi’s diffuse Willmore functional to this variational problem. Our main contribution is a penalisation term which ensures connectedness in the sharp interface limit. The penalisation of disconnectedness is based on a geodesic distance chosen to be small between two… Expand

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