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.
Subscribe to Journal
Get full journal access for 1 year
only $16.58 per issue
All prices are NET prices.
VAT will be added later in the checkout.
Rent or Buy article
Get time limited or full article access on ReadCube.
All prices are NET prices.
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.
Ferren, R. A. Advances in polymeric piezoelectric transducers. Nature 350, 26–27 (1991).
Anderson, J. C. & Eriksson, C. Piezoelectric properties of dry and wet bone. Nature 227, 491–492 (1970).
Priya, S. & Nahm, S. Lead-free Piezoelectrics (Springer, New York, 2011).
Li, F. et al. Ultrahigh piezoelectricity in ferroelectric ceramics by design. Nat. Mater. 17, 349–354 (2018).
Guerin, S. et al. Control of piezoelectricity in amino acids by supramolecular packing. Nat. Mater. 17, 180–186 (2018).
Egusa, S. et al. Multimaterial piezoelectric fibres. Nat. Mater. 9, 643–648 (2010).
Lu, X., Qu, H. & Skorobogatiy, M. Piezoelectric micro- and nanostructured fibers fabricated from thermoplastic nanocomposites using a fiber drawing technique: comparative study and potential applications. ACS Nano 11, 2103–2114 (2017).
Masmanidis, S. C. et al. Multifunctional nanomechanical systems via tunably coupled piezoelectric actuation. Science 317, 780–783 (2007).
Wang, X. et al. Subatomic deformation driven by vertical piezoelectricity from CdS ultrathin films. Sci. Adv. 2, e1600209 (2016).
Ganeshkumar, R., Cheah, C. W., Xu, R., Kim, S.-G. & Zhao, R. A high output voltage flexible piezoelectric nanogenerator using porous lead-free KNbO3 nanofibers. Appl. Phys. Lett. 111, 013905 (2017).
Gafforelli, G., Corigliano, A., Xu, R. & Kim, S.-G. Experimental verification of a bridge-shaped, nonlinear vibration energy harvester. Appl. Phys. Lett. 105, 203901 (2014).
Dagdeviren, C. et al. Conformal piezoelectric systems for clinical and experimental characterization of soft tissue biomechanics. Nat. Mater. 14, 728–736 (2015).
Grupp, D. E. & Goldman, A. M. Giant piezoelectric effect in strontium titanate at cryogenic temperatures. Science 276, 392–394 (1997).
Espinosa, H. D., Bernal, R. A. & Minary-Jolandan, M. A review of mechanical and electromechanical properties of piezoelectric nanowires. Adv. Mater. 24, 4656–4675 (2012).
Laurenti, M. et al. Nanobranched ZnO Structure: p-Type doping induces piezoelectric voltage generation and ferroelectric-photovoltaic effect. Adv Mater 27, 4218–4223 (2015).
Shin, S. H. et al. Lithium-doped zinc oxide nanowires-polymer composite for high performance flexible piezoelectric nanogenerator. ACS Nano 8, 10844–10850 (2014).
Harris, D. T., Burch, M. J., Mily, E. J., Dickey, E. C. & Maria, J. P. Microstructure and dielectric properties with CuO additions to liquid phase sintered BaTiO3 thin films. J. Mater. Res. 31, 1018–1026 (2016).
Nag, S. K. & Agrawal, D. C. Piezoelectric and mechanical-properties of ceria-doped lead zirconate titanate ceramics. J. Mater. Sci. 27, 4125–4130 (1992).
Manna, S., Brennecka, G. L., Stevanović, V. & Ciobanu, C. V. Tuning the piezoelectric and mechanical properties of the AlN system via alloying with YN and BN. J. Appl. Phys. 122, 105101 (2017).
McCall, W. R., Kim, K., Heath, C., La Pierre, G. & Sirbuly, D. J. Piezoelectric nanoparticle-polymer composite foams. ACS Appl. Mater. Inter. 6, 19504–19509 (2014).
Smay, J. E., Tuttle, B. & III, J. C. Piezoelectric and Acoustic Materials for Transducer Applications 305–318 (Springer, Boston, 2008).
Challagulla, K. S. & Venkatesh, T. A. Electromechanical response of piezoelectric foams. Acta Mater. 60, 2111–2127 (2012).
Zheng, X. et al. Ultralight, ultrastiff mechanical metamaterials. Science 344, 1373–1377 (2014).
Bauer, J. et al. Nanolattices: An emerging class of mechanical metamaterials. Adv. Mater. 29, 1701850 (2017).
Hashimoto, K. Y. & Yamaguchi, M. Elastic, piezoelectric and dielectric properties of composite materials. IEEE 1986 Ultras. Symp. 2, 697–702 (1986).
Glushanin, S., Topolov, V. Y. & Krivoruchko, A. V. Features of piezoelectric properties of 0–3 PbTiO3-type ceramic/polymer composites. Mater. Chem. Phys. 97, 357–364 (2006).
Huang, J. H. & Kuo, W. S. Micromechanics determination of the effective properties of piezoelectric composites containing spatially oriented short fibers. Acta Mater. 44, 4889–4898 (1996).
Bowen, C. R. & Topolov, V. Y. Electromechanical Properties In Composites Based On Ferroelectrics 1–202 (Springer, London, 2009).
Nix, E. L. & Ward, I. M. The measurement of the shear piezoelectric coefficients of polyvinylidene fluoride. Ferroelectrics 67, 137–141 (1986).
Wang, H., Zhang, Q. M., Cross, L. E. & Sykes, A. O. Piezoelectric, dielectric, and elastic properties of poly(vinylidene fluoride/trifluoroethylene). J. Appl. Phys. 74, 3394–3398 (1993).
Deshpande, V. S., Ashby, M. F. & Fleck, N. A. Foam topology bending versus stretching dominated architectures. Acta Mater. 49, 1035–1040 (2001).
Cui, H. C., Hensleigh, R., Chen, H. S. & Zheng, X. Y. Additive manufacturing and size-dependent mechanical properties of three-dimensional microarchitected, high-temperature ceramic metamaterials. J. Mater. Res. 33, 360–371 (2018).
Kim, K. et al. 3D optical printing of piezoelectric nanoparticle–polymer composite materials. ACS Nano 8, 9799–9806 (2014).
Singhal, N., Sharma, M. & Mangal, S. K. Optimal placement of piezoelectric patches over a smart structure. Integrated Ferroelectrics 183, 60–90 (2017).
Annamdas, V. G. M. & Soh, C. K. Influence of loading on the near field based passive metamaterial in structural health monitoring. Strut. Health Monit. 1, 633–640 (2015).
He, X. M. et al. Synthetic homeostatic materials with chemo-mechano-chemical self-regulation. Nature 487, 214–218 (2012).
Eliades, S. J. & Wang, X. Q. Neural substrates of vocalization feedback monitoring in primate auditory cortex. Nature 453, 1102–1106 (2008).
Wu, W. Z., Wen, X. N. & Wang, Z. L. Taxel-addressable matrix of vertical-nanowire piezotronic transistors for active and adaptive tactile imaging. Science 340, 952–957 (2013).
Liu, W. et al. Piezoelectric and mechanical properties of CaO reinforced porous PZT ceramics with one-dimensional pore channels. Ceramics Int. 43, 2063–2068 (2017).
Bowen, C. R., Perry, A., Lewis, A. C. F. & Kara, H. Processing and properties of porous piezoelectric materials with high hydrostatic figures of merit. J. Eur. Ceram. Soc. 24, 541–545 (2004).
Wang, J. X. et al. Microstructure, electrical and mechanical properties of MgO nanoparticles—reinforced porous PZT 95/5 ferroelectric ceramics. Ceramics Int. 39, 3915–3919 (2013).
Pu, J. A., Yan, X. J., Jiang, Y. D., Chang, C. E. & Lin, L. W. Piezoelectric actuation of direct-write electrospun fibers. Sensors Actuators A 164, 131–136 (2010).
He, X. J. & Yao, K. Crystallization mechanism and piezoelectric properties of solution-derived ferroelectric poly(vinylidene fluoride) thin films. Appl. Phys. Lett. 89, 112909 (2006).
Babu, I. & de With, G. Highly flexible piezoelectric 0–3 PZT-PDMS composites with high filler content. Composites Sci. Technol. 91, 91–97 (2014).
Fang, L. C., Li, J., Zhu, Z. Y., Orrego, S. & Kang, S. H. Piezoelectric polymer thin films with architected cuts. J. Mater. Res. 33, 330–342 (2018).
Wan, Hu,J. & Park, T. Continuum models for the plastic deformation of octet-truss lattice materials under multiaxial loading. J. Eng. Mater. Technol. 135, 021004 (2013).
Zheng, X. et al. Multiscale metallic metamaterials. Nat. Mater. 15, 1100–1106 (2016).
Netfabb, Netfabb Ultimate 2019 (Autodesk, 2019).
Liu, L., Kamm, P., Garcia-Moreno, F., Banhart, J. & Pasini, D. Elastic and failure response of imperfect three-dimensional metallic lattices: the role of geometric defects induced by Selective Laser Melting. J. Mech. Phys. Solids. 107, 160–184 (2017).
Abaqus, Abaqus 6.14 Documentation (Dassault Systèmes, 2014).
Kar-Gupta, R. & Venkatesh, T. A. Electromechanical response of piezoelectric composites: effects of geometric connectivity and grain size. Acta Mater. 56, 3810–3823 (2008).
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.
The design and material fabrication methods have been submitted for pending US patents.
Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Supplementary Sections 1–14, Supplementary Video Captions 1–5, Supplementary References 1–37, Supplementary Figures 1–24, Supplementary Tables 1–5.
Flexible metamaterial for energy conversion: hand tapping induced voltage response of the N = 12 flexible piezoelectric metamaterial conformally attached onto a curved surface.
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.
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.
Drop-weight impact absorption and self-sensing: drop-weight impact test on the piezoelectric metamaterial comprised of N = 12 node units.
Directionality sensing: real-time voltage output of the piezoelectric infrastructure comprised of stacked architecture under impact coming from 1, 2 and 3 directions.
About this article
Cite this article
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) doi:10.1038/s41563-018-0268-1
Design of lead-free PVDF/CNT/BaTiO3 piezocomposites for sensing and energy harvesting: the role of polycrystallinity, nanoadditives, and anisotropy
Smart Materials and Structures (2020)
Additive Manufacturing (2020)
Journal of Materials Chemistry A (2019)
Advanced Functional Materials (2019)