A highly anisotropic nonlinear elasticity model for vesicles. II. Derivation of the thin bilayer bending theory

Benoit Merlet (1, 2)

1 CMAP - Centre de Mathématiques Appliquées - Ecole Polytechnique
2 LAGA - Laboratoire Analyse, Géométrie et Applications

We study the thin-shell limit of the nonlinear elasticity model for vesicles introduced in part I. We consider vesicles of width 2eps ↓ 0 with elastic energy of order eps^3. In this regime, we show that the limit model is a bending theory for generalized hypersurfaces -- namely, codimension 1 oriented varifolds without boundary. Up to a positive factor, the limit functional is the Willmore energy. In the language of Gamma -convergence, we establish a compactness result, a lower bound result and the matching upper bound in the smooth case.

Mots clés: Calculus of Variation; Gamma -convergence; Willmore functional; Rigidity estimates; Non-linear elasticity; Lipid bilayers

Domaines: Equations aux dérivées partielles [math.AP]

Benoit Merlet. A highly anisotropic nonlinear elasticity model for vesicles. II. Derivation of the thin bilayer bending theory. 2013. ⟨hal-00848552v2⟩