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Rational design of reconfigurable prismatic architected materials


Advances in fabrication technologies are enabling the production of architected materials with unprecedented properties. Most such materials are characterized by a fixed geometry, but in the design of some materials it is possible to incorporate internal mechanisms capable of reconfiguring their spatial architecture, and in this way to enable tunable functionality. Inspired by the structural diversity and foldability of the prismatic geometries that can be constructed using the snapology origami technique, here we introduce a robust design strategy based on space-filling tessellations of polyhedra to create three-dimensional reconfigurable materials comprising a periodic assembly of rigid plates and elastic hinges. Guided by numerical analysis and physical prototypes, we systematically explore the mobility of the designed structures and identify a wide range of qualitatively different deformations and internal rearrangements. Given that the underlying principles are scale-independent, our strategy can be applied to the design of the next generation of reconfigurable structures and materials, ranging from metre-scale transformable architectures to nanometre-scale tunable photonic systems.

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Figure 1: Design strategy to construct 3D prismatic architected materials.
Figure 2: Deformation modes of 3D prismatic architected materials.
Figure 3: Number of degrees of freedom for architected materials based on the 28 uniform tessellations of the 3D space.
Figure 4: Normalized stiffness K/E of prismatic architected materials.
Figure 5: Enhancing the reconfigurability of 3D prismatic architected materials.
Figure 6: Deformation modes of 3D prismatic architected materials with enhanced reconfigurability.


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This work was supported by the Materials Research Science and Engineering Center under NSF Award number DMR-1420570. K.B. also acknowledges support from the National Science Foundation (CMMI-1149456-CAREER). We thank M. Mixe and S. Shuham for assistance in the fabrication of the cardboard prototypes, and R. Wood for the use of his laboratory.

Author information

Authors and Affiliations



J.T.B.O., C.H. and K.B. proposed and designed the research; J.T.B.O. performed the numerical calculations; J.T.B.O., C.H. and J.C.W. designed and fabricated the models; J.T.B.O. performed the experiments; J.T.B.O. and K.B. wrote the paper.

Corresponding author

Correspondence to Katia Bertoldi.

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Competing interests

The authors declare no competing financial interests.

Additional information

Reviewer Information Nature thanks J. Paik, D. Pasini and the other anonymous reviewer(s) for their contribution to the peer review of this work.

Supplementary information

Supplementary Information

This file contains Supplementary Text and Data, which Includes Supplementary Methods, a Supplementary Discussion, Supplementary Figures 1-12, Supplementary Table 1 and additional references. The fabrication approaches used to make the cardboard prototypes and 3D printed prototypes are described. Also described are the numerical algorithm that were implemented in Matlab (i) to predict the number of degrees of freedom and corresponding deformation modes of 3D prismatic architected materials with rigid faces, and (ii) to characterize the elastic response of 3D prismatic architected materials with deformable faces. (PDF 40377 kb)

Supplementary Data

This zipped file contains the Matlab code used to generate the prismatic architected materials and determine their mobility and deformation modes. A detailed description of the code is given in the Supplementary Information. (ZIP 33 kb)

Strategy to design prismatic architected materials

Space-filling and periodic assemblies of convex polyhedra are used as a template to construct prismatic architected materials. After selecting a space-filling tessellation, we focus on a unit cell and separate the polyhedra while ensuring that the normals of all periodically-placed face pairs remain aligned. We then extrude the edges of the polyhedra in the direction normal to their faces to construct the extruded unit cell, which is then used to form the architected material. (MP4 1670 kb)

Reconfigurability of prismatic architected materials

Three prototypes of the 3D prismatic architected materials were constructed using cardboard for the rigid faces and double-sided tape for flexible hinges. Depending on the space-filling assembly of polyhedra used as a template, the resulting architected material has different deformation modes or is completely rigid. (MP4 10101 kb)

Enhancing the reconfigurability of prismatic architected materials.

To alter the reconfigurability of the architected materials, we reduce their connectivity by extruding only selected face pairs of the unit cell, while making the remaining faces rigid. As an example, the architected material based on the space-filling assembly of truncated octahedra can made reconfigurable by extruding only 6 of its faces and making the remaining 8 faces rigid. (MP4 9512 kb)

Different modes observed in prismatic architected materials.

A variety of qualitatively different deformation modes can be achieved in the proposed prismatic architected materials besides shear, including internal reconfigurations that do not alter the macroscopic shape of the materials, and uniform expansion along one or two principal directions. (MP4 8025 kb)

3D printed reconfigurable architected materials.

Using multi-material additive manufacturing we fabricated two of the proposed prismatic architected materials. The faces were fabricated using a rigid material, while the hinges were given a finite size and printed using a softer material. The two architectures that were printed are characterized by respectively zero and one deformation modes. (MP4 7133 kb)

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Overvelde, J., Weaver, J., Hoberman, C. et al. Rational design of reconfigurable prismatic architected materials. Nature 541, 347–352 (2017).

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