TY - JOUR

T1 - Limitations of curvature-induced rigidity

T2 - How a curved strip buckles under gravity

AU - Taffetani, M

AU - Box, F

AU - Neveu, A

AU - Vella, D

PY - 2019/8/14

Y1 - 2019/8/14

N2 - The preference of thin flat sheets to bend rather than stretch, combined with results from geometry, mean that changes in a thin sheet's Gaussian curvature are prohibitively expensive. As a result, an imposed curvature in one principal direction inhibits bending in the other: the so-called curvature-induced rigidity. Here, we study the buckling behaviour of a rectangular strip of finite thickness held horizontally in a gravitational field, but with a transverse curvature imposed at one end. The finite thickness of the sheet limits the efficacy of curvature-induced rigidity in two ways: i) finite bending stiffness acts to "uncurve" the sheet, even if this costs some stretching energy, and ii) for sufficiently long strips, finite weight deforms the strip downwards, releasing some of its gravitational potential energy. We find the critical imposed curvature required to prevent buckling (or, equivalently, to rigidify the strip), determining the dependence on geometrical and constitutive parameters, as well as describing the buckled shape of the strip well beyond the threshold for buckling. In doing so, we quantify the intuitive understanding of curvature-induced rigidity that we gain from curving the crust of a slice of pizza to prevent it from drooping downwards as we eat.

AB - The preference of thin flat sheets to bend rather than stretch, combined with results from geometry, mean that changes in a thin sheet's Gaussian curvature are prohibitively expensive. As a result, an imposed curvature in one principal direction inhibits bending in the other: the so-called curvature-induced rigidity. Here, we study the buckling behaviour of a rectangular strip of finite thickness held horizontally in a gravitational field, but with a transverse curvature imposed at one end. The finite thickness of the sheet limits the efficacy of curvature-induced rigidity in two ways: i) finite bending stiffness acts to "uncurve" the sheet, even if this costs some stretching energy, and ii) for sufficiently long strips, finite weight deforms the strip downwards, releasing some of its gravitational potential energy. We find the critical imposed curvature required to prevent buckling (or, equivalently, to rigidify the strip), determining the dependence on geometrical and constitutive parameters, as well as describing the buckled shape of the strip well beyond the threshold for buckling. In doing so, we quantify the intuitive understanding of curvature-induced rigidity that we gain from curving the crust of a slice of pizza to prevent it from drooping downwards as we eat.

UR - https://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=pure_starter&SrcAuth=WosAPI&KeyUT=WOS:000481854000001&DestLinkType=FullRecord&DestApp=WOS

U2 - 10.1209/0295-5075/127/14001

DO - 10.1209/0295-5075/127/14001

M3 - Letter

SN - 0295-5075

VL - 127

SP - 1

EP - 7

JO - EPL

JF - EPL

IS - 1

M1 - 14001

ER -