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}
}
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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