BPS2026 – Wrinkling in sheets with nonuniform growth and bending rigidity

Wrinkles at the edge of thin elastic sheets are common in natural systems (as in leaves, petals, and sea slugs). Wrinkling arises in these sheets because they bend easily. Here, we investigate wrinkles at edges of isolated bi-strips in which a thin sheet that swells is attached to an adjacent sheet that does not swell. When bending rigidity is uniform across the bi-strip, swelling is known to result in an axisymmetric shape like a wine bottle: two cylinders of different radii joined by a smooth transition zone. However, when the swollen strip has a different bending rigidity than the non-swollen strip, the axisymmetric shape is no longer energetically favorable and wrinkles arise. The wrinkles coarsen with distance from the transition zone, with dimensionless wavelength proportional to the dimensionless width to the power of 2/3. We find that when the bending rigidity of the non-swollen area is larger than that of the swollen area (but not infinite), the non-swollen area has a non-infinite radius of curvature. In this system, wrinkles extend a critical distance beyond the junction of the two strips, where the critical distance is proportional to the radius of curvature. Local wrinkles can decrease the bending energy of the entire system by allowing the non-swollen area to have a larger radius of curvature than would otherwise be dictated by its reference geometry. Our results are relevant to a wide range of sheets that experience non-uniform growth both in natural systems and in synthetic systems such as designed, responsive materials.