Universal formulae for the limiting elastic energy of membrane networks

TL;DR

This paper derives universal formulas for the limiting elastic energies of triangulated membrane networks, improving upon previous models by addressing shape dependence and mesh distortion effects, and providing comprehensive elastic coefficients.

Contribution

It introduces universal formulae for the limiting elastic energies of membrane networks, accounting for finite elasticity and full bending-stretching coupling, with applications to specific geometries.

Findings

Formulas account for shape dependence and mesh distortion effects.

Provides complete set of elastic coefficients for membrane networks.

Demonstrates formulas on cylindrical and spherical networks.

Abstract

We provide universal formulae for the limiting stretching and bending energies of triangulated membrane networks endowed with nearest neighbor bond potentials and cosine-type dihedral angle potentials. The given formulae account for finite elasticity and solve some deficiencies of earlier results for Helfrich-type bending energies, due to shape-dependence and sensitivity to mesh distortion effects of the limiting elastic coefficients. We also provide the entire set of the elastic coefficients characterizing the limiting response of the examined networks, accounting for full bending-stretching coupling. We illustrate the effectiveness of the proposed formulae by way of example, on examining the special cases of cylindrical and spherical networks covered with equilateral triangles, and discussing possible strategies for the experimental characterization of selected elastic moduli.