Vol. 3, No. 2, 2015

Download this article
Download this article For screen
For printing
Recent Issues
Volume 5, Issue 2
Volume 5, Issue 1
Volume 4, Issue 3+4
Volume 4, Issue 2
Volume 4, Issue 1
Volume 3, Issue 4
Volume 3, Issue 3
Volume 3, Issue 2
Volume 3, Issue 1
Volume 2, Issue 2
Volume 2, Issue 1
Volume 1, Issue 2
Volume 1, Issue 1
The Journal
About the Journal
Editorial Board
Submission Guidelines
Submission Form
Ethics Statement
Editorial Login
Author Index
To Appear
ISSN: 2325-3444 (e-only)
ISSN: 2326-7186 (print)
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

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.

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

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