  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.
