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Buffering by buckling as a route for elastic deformation

Nature Reviews Physics volume 1, pages 425–436 (2019)Cite this article

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Abstract

Thin objects are deformed in a range of applications and at a range of scales, from graphene and the actuators used in soft robots to the light sails of spacecraft. Such deformations are constrained, as it is much easier to bend than to stretch a thin object — this constraint is often used to determine the deformations that are allowed and those that are prohibited. Recently, however, a series of applications has emerged in which apparently prohibited deformations are observed. In many of these examples, the apparent ability to stretch and compress (as well as bend) is facilitated by excess material that is stored in microscopic buckled structures: the changes in length that are required to enable particular deformations are ‘buffered by buckling’. In this Review, I discuss buffering by buckling as a means of enabling elastic deformations without significant changes of material length (thereby distinguishing this mechanism from material swelling and growth). I discuss a range of examples from technology and nature and consider the conditions under which buffering by buckling operates.

Key points

  • Thin elastic objects are much easier to bend than to stretch or compress and thus usually deform while preserving their length.

  • Gauss’s Theorema Egregium places severe restrictions on the length-preserving deformations that are possible.

  • The introduction of small-scale buckling structures within a thin object can enable it to access deformation modes that appear to require changes in length: buckles buffer the required change in length.

  • Small-scale buckles are often designed in systems but also emerge naturally through instabilities such as wrinkling.

  • Emergent buckling structures enable changes in curvature, but in turn, the fine structure of the buckling depends on this curvature.

  • Buffering by buckling is an effective mechanism for accommodating apparent changes in length but only operates when an object is extremely slender and subject to intermediate tensions or confinement.

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Fig. 1: Buckling and buffering by buckling.
Fig. 2: Elastic deformation facilitated by the removal of material and insertion of cuts.
Fig. 3: Curvature changes enabled by buffering by buckling of a designed microstructure.
Fig. 4: High-extensibility materials resulting from emergent buffering by buckling.
Fig. 5: Apparent changes in Gaussian curvature enabled by wrinkling.

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Acknowledgements

The author thanks B. Davidovitch and A. Goriely for various discussions and B. Davidovitch, M. Liu and J. Paulsen for comments on an earlier version of this Review. This work is supported by funding from the Leverhulme Trust through a Philip Leverhulme Prize.

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    Dominic Vella

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Glossary

Buckling

Bending or giving way under compression.

Pure bending

Bending without stretching of the centre-line of a surface.

Euler buckling

The buckling of a 1D structure over its whole length and confined to a single plane.

Isometries

Deformations of a surface that preserve distances between points, as measured within the surface.

Gaussian curvature

The product of the principal curvatures of a surface; Gaussian curvature is an intrinsic property of a surface, depending only on distances measured in the surface itself.

Gross shape

The large-scale shape of a thin object, which may be decorated by fine-scale structure such as wrinkles.

Tension-field theory

A limit of the equations of elasticity theory in which objects resist only tensile, not compressive, forces.

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Vella, D. Buffering by buckling as a route for elastic deformation. Nat Rev Phys 1, 425–436 (2019). https://doi.org/10.1038/s42254-019-0063-1

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