Curvature-controlled defect localization in crystalline wrinkling patterns

TL;DR

This study explores how curvature and topology influence defect patterns in crystalline wrinkling, revealing universal scaling laws and local defect behaviors that can be harnessed for advanced material patterning.

Contribution

It demonstrates the universal quadratic scaling of defect numbers and the dependence of defect localization on local curvature in elastic bilayers.

Findings

Total defect count scales quadratically with system size.

Defect localization depends strongly on local Gaussian curvature.

Curvature can be used to control defect patterns in elastic materials.

Abstract

We investigate the influence of curvature and topology on crystalline wrinkling patterns in 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.