D. D. Fox, A. Raoult, and J. C. Simo, A justification of nonlinear properly invariant plate theories, Archive for Rational Mechanics and Analysis, vol.119, issue.18, pp.157-199, 1993.
DOI : 10.1007/BF00375134

H. Le, D. , and A. Raoult, The nonlinear membrane model as variational limit of nonlinear three-dimensional elasticity, J. Math. Pures Appl, vol.74, issue.96, pp.549-578, 1995.

L. Dret and A. Raoult, The membrane shell model in nonlinear elasticity: A variational asymptotic derivation, Journal of Nonlinear Science, vol.27, issue.18, pp.59-84, 1996.
DOI : 10.1007/BF02433810

O. Pantz, On the Justification of the Nonlinear Inextensional Plate Model, Archive for Rational Mechanics and Analysis, vol.167, issue.3, pp.179-209, 2003.
DOI : 10.1007/s00205-002-0238-1

G. Friesecke, R. D. James, and S. Müller, A theorem on geometric rigidity and the derivation of nonlinear plate theory from three-dimensional elasticity, Communications on Pure and Applied Mathematics, vol.120, issue.3, pp.1461-1506, 2002.
DOI : 10.1002/cpa.10048

G. Friesecke, R. D. James, M. G. Mora, and S. Müller, Derivation of nonlinear bending theory for shells from three-dimensional nonlinear elasticity by Gamma-convergence, Comptes Rendus Mathematique, vol.336, issue.8, pp.697-702, 2003.
DOI : 10.1016/S1631-073X(03)00028-1

S. Conti, F. Maggi, and S. Müller, Rigorous Derivation of F??ppl???s Theory for Clamped Elastic Membranes Leads to Relaxation, SIAM Journal on Mathematical Analysis, vol.38, issue.2, pp.657-680, 2006.
DOI : 10.1137/050632567

G. Friesecke, R. D. James, and S. Müller, A Hierarchy of Plate Models Derived from Nonlinear Elasticity by Gamma-Convergence, Archive for Rational Mechanics and Analysis, vol.180, issue.2, pp.183-236, 2006.
DOI : 10.1007/s00205-005-0400-7

S. Conti and F. Maggi, Confining Thin Elastic Sheets and Folding Paper, Archive for Rational Mechanics and Analysis, vol.41, issue.2, pp.1-48, 2008.
DOI : 10.1007/s00205-007-0076-2

P. B. Canham, The minimum energy of bending as a possible explanation of the biconcave shape of the human red blood cell, Journal of Theoretical Biology, vol.26, issue.1, pp.61-8180032, 1970.
DOI : 10.1016/S0022-5193(70)80032-7

W. Helfrich, Abstract, Zeitschrift f??r Naturforschung C, vol.28, issue.11-12, pp.693-703, 1973.
DOI : 10.1515/znc-1973-11-1209

E. A. Evans, Bending Resistance and Chemically Induced Moments in Membrane Bilayers, Biophysical Journal, vol.14, issue.12, pp.923-931, 1974.
DOI : 10.1016/S0006-3495(74)85959-X

J. T. Jenkins, The Equations of Mechanical Equilibrium of a Model Membrane, SIAM Journal on Applied Mathematics, vol.32, issue.4, pp.755-764, 1977.
DOI : 10.1137/0132063

S. J. Singer and G. L. Nicolson, The Fluid Mosaic Model of the Structure of Cell Membranes, Science, vol.175, issue.4023, pp.720-731, 1972.
DOI : 10.1126/science.175.4023.720

D. J. Steigmann, Fluid films with curvature elasticity Archive for Rational Mechanics and Analysis, pp.127-152, 1999.

S. Svetina and B. Ek, Membrane bending energy and shape determination of phospholipid vesicles and red blood cells, European Biophysics Journal, vol.10, issue.2, pp.101-111, 1989.
DOI : 10.1007/BF00257107

U. Seifert, K. Berndl, and R. Lipowsky, Shape transformations of vesicles: Phase diagram for spontaneous- curvature and bilayer-coupling models, Physical Review A, vol.44, issue.2, pp.1182-1202, 1991.
DOI : 10.1103/PhysRevA.44.1182

L. Miao, U. Seifert, M. Wortis, and H. Döbereiner, Budding transitions of fluid-bilayer vesicles: The effect of area-difference elasticity, Physical Review E, vol.49, issue.6, pp.5389-5407, 1994.
DOI : 10.1103/PhysRevE.49.5389

S. Krishnaswamy, A cosserat-type model for the red blood cell wall, International Journal of Engineering Science, vol.34, issue.8, pp.873-899, 1996.
DOI : 10.1016/0020-7225(95)00139-5

H. J. Deuling and W. Helfrich, The curvature elasticity of fluid membranes : A catalogue of vesicle shapes, Journal de Physique, vol.37, issue.11, pp.1335-1345, 1976.
DOI : 10.1051/jphys:0197600370110133500

URL : https://hal.archives-ouvertes.fr/jpa-00208531

J. T. Jenkins, Static equilibrium configurations of a model red blood cell, Journal of Mathematical Biology, vol.13, issue.2, pp.149-169, 1977.
DOI : 10.1007/BF00275981

J. C. Luke, A Method for the Calculation of Vesicle Shapes, SIAM Journal on Applied Mathematics, vol.42, issue.2, pp.333-345, 1982.
DOI : 10.1137/0142026

J. C. Luke and J. I. Kaplan, On the Theoretical Shapes of Bilipid Vesicles under Conditions of Increasing Membrane Area, Biophysical Journal, vol.25, issue.1, pp.107-111, 1979.
DOI : 10.1016/S0006-3495(79)85280-7

A. Agrawal and D. Steigmann, Boundary-value problems in the theory of lipid membranes, Continuum Mechanics and Thermodynamics, vol.4, issue.1, pp.57-82, 2009.
DOI : 10.1007/s00161-009-0102-8

F. Feng and W. S. Klug, Finite element modeling of lipid bilayer membranes, Journal of Computational Physics, vol.220, issue.1, pp.394-408, 2006.
DOI : 10.1016/j.jcp.2006.05.023

A. Bonito, R. H. Nochetto, and M. S. Pauletti, Parametric FEM for geometric biomembranes, Journal of Computational Physics, vol.229, issue.9, pp.3171-3188, 2010.
DOI : 10.1016/j.jcp.2009.12.036

A. Bonito, R. H. Nochetto, and M. S. Pauletti, Dynamics of Biomembranes: Effect of the Bulk Fluid, Mathematical Modelling of Natural Phenomena, vol.6, issue.5, pp.25-43, 2011.
DOI : 10.1051/mmnp/20116502

G. Dziuk, Computational parametric Willmore flow, Numerische Mathematik, vol.14, issue.1, pp.55-80, 2008.
DOI : 10.1007/s00211-008-0179-1

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.219.1944

Z. Peng, X. Li, I. V. Pivkin, M. Dao, G. E. Karniadakis et al., Lipid bilayer and cytoskeletal interactions in a red blood cell, Proceedings of the National Academy of Sciences, vol.110, issue.33, 2013.
DOI : 10.1073/pnas.1311827110

Q. Du, C. Liu, and X. Wang, Simulating the deformation of vesicle membranes under elastic bending energy in three dimensions, Journal of Computational Physics, vol.212, issue.2, pp.757-777, 2006.
DOI : 10.1016/j.jcp.2005.07.020

Q. Du, C. Liu, and X. Wang, A phase field approach in the numerical study of the elastic bending energy for vesicle membranes, Journal of Computational Physics, vol.198, issue.2, pp.450-468, 2004.
DOI : 10.1016/j.jcp.2004.01.029

Q. Du and J. Zhang, Adaptive Finite Element Method for a Phase Field Bending Elasticity Model of Vesicle Membrane Deformations, SIAM Journal on Scientific Computing, vol.30, issue.3, pp.1634-1657, 2008.
DOI : 10.1137/060656449

K. Shravan, D. Veerapaneni, D. Gueyffier, G. Zorin, and . Biros, A boundary integral method for simulating the dynamics of inextensible vesicles suspended in a viscous fluid in 2D, J. Comput. Phys, vol.228, issue.7, pp.2334-2353, 2009.

J. Sun-sohn, Y. Tseng, S. Li, A. Voigt, and J. S. Lowengrub, Dynamics of multicomponent vesicles in a viscous fluid, Journal of Computational Physics, vol.229, issue.1, pp.119-144, 2010.
DOI : 10.1016/j.jcp.2009.09.017

Y. Kim and M. Lai, Simulating the dynamics of inextensible vesicles by the penalty immersed boundary method, Journal of Computational Physics, vol.229, issue.12, pp.4840-4853, 2010.
DOI : 10.1016/j.jcp.2010.03.020

Y. Liu, L. Zhang, X. Wang, and W. Liu, Coupling of Navier-Stokes equations with protein molecular dynamics and its application to hemodynamics, International Journal for Numerical Methods in Fluids, vol.85, issue.12, pp.1237-1252, 2004.
DOI : 10.1002/fld.798

Y. Liu and W. Liu, Rheology of red blood cell aggregation by computer simulation, Journal of Computational Physics, vol.220, issue.1, pp.139-154, 2006.
DOI : 10.1016/j.jcp.2006.05.010

M. Lindsay, A. L. Crowl, and . Fogelson, Computational model of whole blood exhibiting lateral platelet motion induced by red blood cells, Int. J. Numer. Methods Biomed. Eng, vol.26, pp.3-4471, 2010.

D. Salac and M. Miksis, A level set projection model of lipid vesicles in general flows, Journal of Computational Physics, vol.230, issue.22, pp.8192-8215, 2011.
DOI : 10.1016/j.jcp.2011.07.019

E. Maitre, T. Milcent, G. Cottet, A. Raoult, and Y. Usson, Applications of level set methods in computational biophysics, Mathematical and Computer Modelling, vol.49, issue.11-12, pp.11-122161, 2009.
DOI : 10.1016/j.mcm.2008.07.026

URL : https://hal.archives-ouvertes.fr/hal-00177593

V. Doyeux, Y. Guyot, V. Chabannes, C. Prud-'homme, and M. Ismail, Simulation of two-fluid flows using a finite element/level set method. Application to bubbles and vesicle dynamics, Journal of Computational and Applied Mathematics, vol.246, pp.251-259, 2013.
DOI : 10.1016/j.cam.2012.05.004

URL : https://hal.archives-ouvertes.fr/hal-01345573

B. Merlet, A highly anisotropic nonlinear elasticity model for vesicles I. Eulerian formulation, rigidity estimates and vanishing energy limit. 23 pages, preprint, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00848547

B. Merlet, A highly anisotropic nonlinear elasticity model for vesicles. II. Derivation of the thin bilayer bending theory. 57 pages, preprint, 2013.
URL : https://hal.archives-ouvertes.fr/hal-00848552

C. and U. Cnrs, Ecole Polytechnique, 91128 Palaiseau Cedex, France E-mail address: olivier.pantz@polytechnique.org URL: http://www.cmap.polytechique.fr DRI, Institut Polytechnique des Sciences Avancées, 5-9 rue Maurice Grandcoing, 94200 Ivry-sur-Seine