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Three-dimensional printing of piezoelectric materials with designed anisotropy and directional response


Piezoelectric coefficients are constrained by the intrinsic crystal structure of the constituent material. Here we describe design and manufacturing routes to previously inaccessible classes of piezoelectric materials that have arbitrary piezoelectric coefficient tensors. Our scheme is based on the manipulation of electric displacement maps from families of structural cell patterns. We implement our designs by additively manufacturing free-form, perovskite-based piezoelectric nanocomposites with complex three-dimensional architectures. The resulting voltage response of the activated piezoelectric metamaterials at a given mode can be selectively suppressed, reversed or enhanced with applied stress. Additionally, these electromechanical metamaterials achieve high specific piezoelectric constants and tailorable flexibility using only a fraction of their parent materials. This strategy may be applied to create the next generation of intelligent infrastructure, able to perform a variety of structural and functional tasks, including simultaneous impact absorption and monitoring, three-dimensional pressure mapping and directionality detection.

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Fig. 1: Design of piezoelectric metamaterials for tailorable piezoelectric charge constants.
Fig. 2: Surface functionalization of PZT with photosensitive monomers and 3D printing of piezoelectric metamaterials with complex micro-architectures.
Fig. 3: Measurement of 3D piezoelectric responses.
Fig. 4: Assembly of architected metamaterial blocks as intelligent infrastructures.
Fig. 5: Force directionality sensing.

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Data availability

All data generated during this study are included within the paper and its Supplementary Information files and/or are available from the corresponding author upon request.


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We acknowledge funding from the ICTAS Junior Faculty Award, NSF CMMI 1727492, the Air Force Office of Scientific Research (FA9550-18-1-0299) and the Office of Naval Research (N00014-18-1-2553) for supporting this work. D.M. and S.P. acknowledge the financial support from NSF through award IIP-1832179. P.M. and M.G.K. are thankful for the support from Air Force Office of Scientific Research through grant FA9550-18-1-0233. We thank E. Ventrella, R. Mondschein and Dr. T. Long for help with collecting PZT particle diameter data, A. Wei, K. Jung, H. Chen, and Z. Xu for assitance with analysis and fabrication.

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Authors and Affiliations



X.Z. conceived and designed the research. R.H. synthesized the functionalized piezoelectric materials and functionalization measurement. H.C. fabricated samples, performed testing and data analysis. D.Y. and H.C. designed the models and performed the analytical and numerical calculations. H.C., R.H. and X.Z. developed the materials and fabrication methods. D.Y., H.C. and X.Z. developed the method for manipulating anisotropy. D.M., P.K., M.G.K. and S.P. developed the poling method and contributed to the testing of the piezoelectric properties of the 3D metamaterials. H.C., R.H., D.Y. and X.Z. wrote the manuscript with input from all authors. All authors participated in drafting the manuscript, discussion and interpretation of the data.

Corresponding author

Correspondence to Xiaoyu (Rayne) Zheng.

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Competing interests

The design and material fabrication methods have been submitted for pending US patents.

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Supplementary information

Supplementary Information

Supplementary Sections 1–14, Supplementary Video Captions 1–5, Supplementary References 1–37, Supplementary Figures 1–24, Supplementary Tables 1–5.

Supplementary Video 1

Flexible metamaterial for energy conversion: hand tapping induced voltage response of the N = 12 flexible piezoelectric metamaterial conformally attached onto a curved surface.

Supplementary Video 2

Flexible 3D ring-like piezo-sensor: a ring-like sensor was prepared and tested to show the signal generated during the folding and unfolding process of human figures.

Supplementary Video 3

Directional voltage response: real-time voltage outputs of piezoelectric metamaterials comprising N = 5 node unit with θθ = 75°, 90° and 120° under impact coming from 1, 2 and 3 directions.

Supplementary Video 4

Drop-weight impact absorption and self-sensing: drop-weight impact test on the piezoelectric metamaterial comprised of N = 12 node units.

Supplementary Video 5

Directionality sensing: real-time voltage output of the piezoelectric infrastructure comprised of stacked architecture under impact coming from 1, 2 and 3 directions.

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Cui, H., Hensleigh, R., Yao, D. et al. Three-dimensional printing of piezoelectric materials with designed anisotropy and directional response. Nature Mater 18, 234–241 (2019).

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