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