膜网络极限弹性能的通用公式
Universal formulae for the limiting elastic energy of membrane networks
摘要：
我们提供了具有最近邻键势和余弦型二面角势的三角形膜网络的极限拉伸能和极限弯曲能的普遍公式。给出的公式考虑有限的弹性和解决一些不足的早期结果Helfrich型弯曲能量，由于形状依赖性和敏感性网格变形的影响的限制弹性系数。我们还提供了一整套的弹性系数，其特征在于所检查的网络的极限响应，占充分的弯曲拉伸耦合。我们举例说明了所提出的公式的有效性，在检查的特殊情况下，圆柱形和球形网络覆盖等边三角形，并讨论可能的策略选择的弹性模量的实验表征。
英文摘要：
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.
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