Exact Solution for Elastic Networks on Curved Surfaces
Exact Solution for Elastic Networks on Curved Surfaces
复制标题
曲面上弹性网络的精确解
DOI：
10.1103/physrevlett.129.088001
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发表时间：
2022
影响因子：
8.6
通讯作者：
Travesset, Alex
中科院分区：
文献类型：
--
作者：
Dong, Yinan;Zandi, Roya;Travesset, Alex
描述一个被约束在冻结曲面上的弹性网络结构的问题出现在许多科学领域，并且已经通过许多不同的方法来解决，最值得注意的是，扩展线弹性或通过有效的缺陷相互作用模型。在这封信中，我们表明，可以解决的问题，考虑非线性弹性在一个精确的形式，而不诉诸任何近似的几何量。通过这种方式，我们能够考虑过去难以处理或不可行的不同影响，例如有限的线张力，对泊松比的明确依赖，或整个晶格的粒子位置的确定。对几种具有旋转对称的几何图形进行了显式求解。与线性弹性的比较揭示了一种超越其严格适用范围的一致性。还讨论了病毒组装表征问题的含义。
The problem of characterizing the structure of an elastic network constrained to lie on a frozen curved surface appears in many areas of science and has been addressed by many different approaches, most notably, extending linear elasticity or through effective defect interaction models. In this Letter, we show that the problem can be solved by considering nonlinear elasticity in an exact form without resorting to any approximation in terms of geometric quantities. In this way, we are able to consider different effects that have been unwieldy or not viable to include in the past, such as a finite line tension, explicit dependence on the Poisson ratio, or the determination of the particle positions for the entire lattice. Several geometries with rotational symmetry are solved explicitly. Comparison with linear elasticity reveals an agreement that extends beyond its strict range of applicability. Implications for the problem of the characterization of virus assembly are also discussed.