caa a22 4500 605515638 CHVBK 20210128100710.0 cr unu---uuuuu 210128e20150801xx s 000 0 eng 10.1007/s00205-014-0840-z doi (NATIONALLICENCE)springer-10.1007/s00205-014-0840-z Merlet Benoît Centre de Mathématiques Appliquées (CMAP), Ecole Polytechnique, 91128, Palaiseau, France aut A Highly Anisotropic Nonlinear Elasticity Model for Vesicles II: Derivation of the Thin Bilayer Bending Theory [Elektronische Daten] [Benoît Merlet] We study the thin-shell limit of the nonlinear elasticity model for vesicles introduced in part I. We consider vesicles of width $${2 \varepsilon \downarrow 0}$$ 2 ε ↓ 0 with elastic energy of order $${\varepsilon^3}$$ ε 3 . In this regime, we show that the limit model is a bending theory for generalized hypersurfaces—namely, co-dimension one oriented varifolds without boundary. Up to a positive factor, the limit functional is the Willmore energy. In the language of $${{\it \Gamma}}$$ Γ -convergence, we establish a compactness result, a lower bound result and the matching upper bound in the smooth case. Springer-Verlag Berlin Heidelberg, 2015 Archive for Rational Mechanics and Analysis Springer Berlin Heidelberg 217/2(2015-08-01), 681-740 0003-9527 217:2<681 2015 217 205 https://doi.org/10.1007/s00205-014-0840-z text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00205-014-0840-z text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Merlet Benoît Centre de Mathématiques Appliquées (CMAP), Ecole Polytechnique, 91128, Palaiseau, France aut NATIONALLICENCE 773 0- Archive for Rational Mechanics and Analysis Springer Berlin Heidelberg 217/2(2015-08-01), 681-740 0003-9527 217:2<681 2015 217 205