Jiménez Francisco López, Stoop Norbert, Lagrange Romain, Dunkel Jörn, Reis Pedro M
Department of Civil & Environmental Engineering, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139-4307, USA.
Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, Massachusetts 02139-4307, USA.
Phys Rev Lett. 2016 Mar 11;116(10):104301. doi: 10.1103/PhysRevLett.116.104301. Epub 2016 Mar 7.
We investigate the influence of curvature and topology on crystalline dimpled patterns on the surface of generic elastic bilayers. Our numerical analysis predicts that the total number of defects created by adiabatic compression exhibits universal quadratic scaling for spherical, ellipsoidal, and toroidal surfaces over a wide range of system sizes. However, both the localization of individual defects and the orientation of defect chains depend strongly on the local Gaussian curvature and its gradients across a surface. Our results imply that curvature and topology can be utilized to pattern defects in elastic materials, thus promising improved control over hierarchical bending, buckling, or folding processes. Generally, this study suggests that bilayer systems provide an inexpensive yet valuable experimental test bed for exploring the effects of geometrically induced forces on assemblies of topological charges.
我们研究了曲率和拓扑结构对一般弹性双层膜表面晶体酒窝图案的影响。我们的数值分析预测，在广泛的系统尺寸范围内，绝热压缩产生的缺陷总数对于球形、椭圆形和环形表面呈现出普遍的二次标度关系。然而，单个缺陷的定位以及缺陷链的取向都强烈依赖于局部高斯曲率及其在整个表面上的梯度。我们的结果表明，曲率和拓扑结构可用于在弹性材料中对缺陷进行图案化，从而有望更好地控制分层弯曲、屈曲或折叠过程。总体而言，这项研究表明双层系统为探索几何诱导力对拓扑电荷集合体的影响提供了一个廉价但有价值的实验测试平台。
