Buckling in 3D structures

Fully 3D porous structures have been shown to be potentially useful in a wide range of fields, including structural applications, photonics, tissue engineering, sensing, and catalysis. The introduction of actuation mechanisms and buckling within these structures may lead to a new generation of efficient materials and devices capable of multiple shapes for multiple functions. Straightforward generalization of a 2D square array of circular holes to a simple cubic arrangement of spherical pores leads to the design of structures that do not show a truly 3D response at instability.

Six different cubic crystals can be built using Buckliballs as a building block.

To design volumetric 3D materials where buckling still acts as actuation mechanism, we are using the Buckliball as a building block to tessellate the space. We identified procedures to guide the selection of both the building blocks and their arrangement, leading to the design of 3D soft and active metamaterials with tunable properties, where buckling still acts as a functional mode of actuation.

Noting that each Buckliball has a limited number of sites between the thin ligaments where it can be attached to other building block, we focused on cubic crystal systems (i.e. sc, bcc, fcc) and identified six different crystals that can be built using Buckliballs as building blocks. In all of these crystals mechanical instabilities act as a functional mode of actuation and introduce dramatic changes into the architectures, while keeping the structure periodic.

Focusing on a 3D array of six-hole buckliballs arranged on a \emph{bcc} lattice, we investigated the response of the structure both experimentally and numerically. We used Finite Elements simulations to investigate the response of structures characterized by a range of different geometric parameters (i.e. porosity, shell thickness and pore shape) and identify a region in the design space where the desired motion is achieved (by preventing instabilities with long wavelength, typical of solid foams). Once the design was finalized, a mold was fabricated using the 3D printer at the Wyss Institute to cast one-half of a spherical shell. 91 identical Buckliballs were assembled together into the crystal. Recently, we tested the response of this soft crystal under uniaxial compression and visualized the deformation of the microstructure at different level of the applied deformation using a Micro-CT System. The experiments confirm that above a critical level of deformation the crystals undergo a structural transformation (induced by buckling) that alters the periodicity of the structure. Interestingly, this transformation also results in a contraction of the material in the direction perpendicular the applied deformation, indicating that our 3D soft metamaterial is characterized by an auxetic behavior (i.e. Negative Poisson's ratio). Moreover, our preliminary results show an excellent agreement between experiments and simulations, not only from a qualitative, but also from a quantitative point of view.

Currently, we  are also  investigating the effect of instabilities and large deformation of these 3D periodic materials on the phononic band gaps as well as the preferential propagation directions of elastic waves.

CT Xray images of a 3D array of six-hole buckliballs arranged on a bcc lattice. (A) and (B) Isometric view ,(C) and (D) cross-sectional views of undeformed and deformed structure. (E) and (F) are magnified views of the innermost RVE taken from CT Xray scanning (in the black box) along with the pictures taken from simulation (red pictures)


  • S. Babee*, J. Shim*, J. Weaver, and K. Bertoldi (* equal contribution).  3D Soft auxetic metamaterials.  Advanced Materials, 2013.