Tuning the mechanical properties of elastic structures is an ongoing endeavor. Established strategies include composites and metamaterials. We propose a novel strategy to tune these properties by introducing geometrical frustration.
In this work, we study the mechanical properties of a frustrated elastic ribbon spring—the non-Euclidean minimal spring. This spring belongs to the family of non-Euclidean plates: it has no spontaneous curvature, but its lateral intrinsic geometry is described by a non-Euclidean reference metric. The reference metric of the minimal spring is hyperbolic and can be embedded as a minimal surface. We argue that the existence of a continuous set of such isometric minimal surfaces with different extensions leads to a complete degeneracy of the bulk elastic energy of the minimal spring under elongation
This degeneracy is removed only by boundary layer effects. As a result, the mechanical properties of the minimal spring are unusual: the spring is ultrasoft with a rigidity that depends on the thickness t as t7/2 and does not explicitly depend on the ribbon’s width. Moreover, we show that as the ribbon is widened, the rigidity may even decrease. These predictions are confirmed by a numerical study of a constrained spring.
I. Levin, and E. Sharon. Anomalously Soft Non-Euclidean Springs. Phys. Rev. Lett. 2015 116(3)