Inclined Auxetic Metamaterials: Buckling



Our earlier work on Auxetic Surfaces was based on the in-plane buckling of elastomeric surfaces caused by hinges oriented normal to the base surface. This current work titled Inclined Auxetics : Buckling  was an opportunistic approach which arose when the hinges were oriented at an angle (inclined) to the base surface. Based on the nature of the hinges Inclined Auxetic structures can be further sub-categorized into buckling based and kinematic based. 

Images showing difference in the hinge orientation between regular auxetic surfaces and inclined auxetic surfaces
Difference in the hinge orientation between regular auxetic surfaces and inclined auxetic surfaces
Two subcatagories of Inclined Auxetics viz. Buckling and kinematic
Sub-categories of Inclined Auxetics


Our metamaterial is obtained from conceptually slicing an extruded block of elastomer with cylindrical holes (regular auxetic metamaterial at an angle θ).Thin sheets of the same elastomer are used to sea Channels on the top and bottom of the metamaterial are used to vacuum air and deploy it.

The change in the angle enables the hinges to be inclined causing the buckling to go out-of-plane and hence changing a flat surface to a textured one

Different values of  θ result in varying levels of out-of-plane deformations.





Light Diffusion

Since the buckling-induced textures have identical morphologies, but an out-of-plane amplitude that monotonically increases with θ, below we will only consider the metamaterials with θ=0 and θ=45. These two configurations provide the maximum difference in 3D deformation, and therefore represent the best candidates for demonstrating how the buckling-induced textures can be leveraged to modulate additional functionalities of these metamaterials, such as light diffusion and friction.


Changes in surface morphology can also translate into changes in frictional properties of a structure. Beyond the ability of these metamaterials to generate large-scale out-of-plane surface geometries, this behavior also offers the opportunity to expose/retract a third material, leading to a tunable Coefficient of Friction(μ)For example, if we simply attach small acrylic spheres in the areas of the surface that retract during buckling , such elements (i) dominate the contact properties in the initial configuration and (ii) disengage with the substrate under vacuum, which then comes in contact with the elastomer.

Application: Soft Robotic Crawler

To demonstrate friction control, we created a soft crawling robot that harnesses the switchable frictional properties of our metamaterial to achieve locomotion.


MaP+S Group at Harvard GSD: Saurabh A Mhatre, Olga Mesa and Martin Bechthold.

Bertoldi Group at Harvard SEAS: Matheus C. Fernandes, Antonio E. Forte, Bing Zhao, James Weaver and Katia Bertoldi. 

This work was supported by NSF-GRFP Fellowship Grant Number DGE-1144152 (M.C.F.), a GEM Consortium Fellowship (M.C.F.) and the Harvard Graduate Prize Fellowship (M.C.F.), and was partially supported by the NSF through the Harvard University Materials Research Science and Engineering Center Grant Number DMR-2011754 and NSF DMREF Grant Number DMR-1922321. We also thank Mohamed Zanaty for insightful discussions and Bolei Deng for assisting with point tracking algorithm.



Featured on the Front Cover of Extreme Mechanics Letters journal (Issue 51)

Matheus C. Fernandes†, Saurabh Mhatre†, Antonio E. Forte, Bing Zhao, Olga Mesa, James C. Weaver, Martin Bechthold, Katia Bertoldi,
Surface texture modulation via buckling in porous inclined mechanical metamaterials, Extreme Mechanics Letters, Volume 51,2022,101549,ISSN 2352-4316, (Link)


Harvard School of Engineering and Applied Sciences : Link Link