Vol. 3, No. 2, 2015
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Derivation of nonlinear shell models combining shear and flexure: application to biological membranes

Olivier Pantz and Karim Trabelsi

Vol. 3 (2015), No. 2, 101–138
DOI: 10.2140/memocs.2015.3.101
Abstract

Biological membranes are often idealized as incompressible elastic surfaces whose strain energy only depends on their mean curvature and possibly on their shear. We show that this type of model can be derived using a formal asymptotic method by considering biological membranes to be thin, strongly anisotropic, elastic, locally homogeneous bodies.

Keywords
shell, nonlinear elasticity, Helfrich, red blood cell, vesicle
Mathematical Subject Classification 2010
Primary: 74K20, 74K25, 74B20
Milestones
Received: 24 July 2012
Revised: 6 June 2014
Accepted: 9 June 2014
Published: 16 May 2015

Communicated by Gilles A. Francfort
Authors
Olivier Pantz
Centre de Mathématiques Appliquées
École Polytechnique
Route de Saclay
91128 Palaiseau CEDEX
France
Karim Trabelsi
Direction du la Recherche et de l’Innovation
Institut Polytechnique des Sciences Avancées
5-9 rue Maurice Grandcoing
94200 Ivry-sur-Seine
France