TY - JOUR
T1 - Anomalously Soft Non-Euclidean Springs
AU - Levin, Ido
AU - Sharon, Eran
N1 - Publisher Copyright:
© 2016 American Physical Society.
PY - 2016/1/20
Y1 - 2016/1/20
N2 - 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. This work is the first to address the unusual mechanical properties of constrained non-Euclidean elastic objects.
AB - 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. This work is the first to address the unusual mechanical properties of constrained non-Euclidean elastic objects.
UR - http://www.scopus.com/inward/record.url?scp=84956697097&partnerID=8YFLogxK
U2 - 10.1103/PhysRevLett.116.035502
DO - 10.1103/PhysRevLett.116.035502
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AN - SCOPUS:84956697097
SN - 0031-9007
VL - 116
JO - Physical Review Letters
JF - Physical Review Letters
IS - 3
M1 - 035502
ER -