Fig. 1 Piezoelectric strain matrix with full nonzero elements dij by metamaterial design in contrast with only five nonzero ones in natural piezoelectric ceramics. (A) Because of similar 6-mm symmetry of natural piezoelectric ceramics, only five nonzero elements in the piezoelectric strain matrix of natural piezoelectric ceramics exist, namely, d31 (equal to d32), d33, and d15 (equal to d24), with the other 13 elements being totally zero. (B) In this work, the 13 nonzero effective piezoelectric coefficients are created by metamaterial design. The method actually achieves macroscopically quasi-symmetry breaking and obtains apparently reduced symmetry.
Fig. 2 Schematic designs of piezoelectric metamaterials. With programmed polarization and applied electric field of subunits, the metamaterials realize all effective normal or shear-strain modes in both quasi-static and resonant frequencies. (A to G) Schematic metamaterial designs and deformation states by finite element simulation in both resonant (with ▲ label) and quasi-static (without ▲ label) states of d11 (d22) mode (A), d13 (d23) mode (B), d12 (d21) mode (C), d14 (d16) mode (D), d16 (d26) mode (E), d34 (d35) mode (F), and d36 mode (G). (H and I) Diagrams of two kinds of fundamental design mechanism learned from natural structures we established, namely, CEE for effective normal strain (H) and DTE for shear strain (I).
Fig. 3 Magnitudes and variation tendency of effective piezoelectric coefficients of diverse metamaterials by FEM simulation. (A) Geometrical diagram and boundary conditions of metamaterials for FEM simulation. For normal-strain modes, two side surfaces parallel to objective strain are fixed as zero-displacement boundary. Center displacement along thickness direction behaves as effective output (with “*” label). While in shear-strain modes, a side surface is fixed and metamaterials show apparent shear deformation. Effective piezoelectric coefficients are calculated based on the motion point (a vertex “*”). (B to F) PNN-PZT, PZT-5H, and PZT-8 chosen as demoed materials; the magnitudes and corresponding variation tendency of artificial piezoelectric coefficients along with geometry sizes are revealed by finite element simulation, which are d11 (d22, d13, and d23) (B), d12 (d21) (C), d14 (d16) and d16 (d26) (D), d34 (d35) (E), and d36 (F) modes.
Fig. 4 Experimental verification of metamaterials with effective piezoelectric coefficients d11 (on behalf of normal strain and CEE) and d36 (on behalf of shear strain and DTE). (A) Schematic diagram of test system for measuring the displacement performance of metamaterials. The system consists of a driving signal module and a high-precision displacement measuring module. (B and C) Real-time displacement responses (B) and amplitudes (C) of d11 mode metamaterial (with LTR = 40) under sinusoidal driving signals with diverse voltages. (D and E) Real-time displacement responses (D) and amplitudes (E) of d36 mode metamaterial (with TLR = 1/14). Photo credit: Jikun Yang, Department of Materials Science and Engineering, College of Engineering, Peking University, Beijing 100871, China.
Fig. 5 Designs of arrayed electromechanical metamaterials and brand-new co-firing shear-mode actuators. (A to C) Arrayed normal-strain metamaterial (length × width × thickness: 2 cm × 2 cm × 1 cm; 20 layers, PNN-PZT) based on novel d11 mode elements and fork-type arrangement ways shows a very large apparent displacement (over 40 μm). (D to F) The puzzling problems of co-fired shear-mode multilayer structure are expected to be solved. On the basis of new fundamental d36 normal-strain–derived shear-mode metamaterials and specific interdigital electrodes (D and E), multilayer shear-mode co-fired structures are designed, exciting perfect shear deformation (F).
- Table 1 Simulated prediction and experimental results of effective piezoelectric coefficients of all seven types of metamaterials based on a kind of commercialized PZT-5H ceramics.
Several experimental results are even bigger than the simulated ones because of an additional shear-bending amplification effect.
Neotype modes Specimen sizes
(length × width × thickness)Simulation values
(pm/V)Experiment values
(pm/V)d11 (LTR = 40) 20 mm × 7 mm × 0.5 mm 16,000 13,592 d13 (LTR = 28) 14 mm × 7 mm × 0.5 mm 11,200 6,984 d12 (LTR = 14) 14 mm × 14 mm × 1 mm 200 2,205 d14 (TLR = 0.1) 10 mm × 10 mm × 1 mm 28 64 d16 (TLR = 0.1) 10 mm × 10 mm × 1 mm 22 37 d34 (TLR = 0.1) 10 mm × 10 mm × 1 mm 531 714 d36 (TLR = 1/14) 14 mm × 14 mm × 1 mm 372 259
Supplementary Materials
Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/5/11/eaax1782/DC1
Section S1. Designing piezoelectric metamaterials with normal-strain mode
Section S2. Designing piezoelectric metamaterials with shear-strain mode
Section S3. Piezoelectric metamaterials composed of multiple meta-atoms
Section S4. FEM simulation details
Section S5. Experimental verification details
Section S6. Arrayed metamaterials with enhanced performance
Section S7. Design of neotype co-firing multilayer shear-mode actuators
Fig. S1. d34 mode piezoelectric metamaterials composed of various numbers of meta-atoms.
Fig. S2. Specimen photographs of all seven kinds of piezoelectric metamaterials.
Fig. S3. Test system for measuring effective displacement outputs of metamaterials.
Fig. S4. Displacement responses to electric field of other five kinds of metamaterials.
Fig. S5. Arrayed shear-mode metamaterials with in-plane arrangement way.
Fig. S6. Preparation processes of neotype co-firing shear-mode multilayer actuator.
Table S1. Schematic diagrams and definition formulas for calculating all effective piezoelectric coefficients.
Additional Files
Supplementary Materials
This PDF file includes:
- Section S1. Designing piezoelectric metamaterials with normal-strain mode
- Section S2. Designing piezoelectric metamaterials with shear-strain mode
- Section S3. Piezoelectric metamaterials composed of multiple meta-atoms
- Section S4. FEM simulation details
- Section S5. Experimental verification details
- Section S6. Arrayed metamaterials with enhanced performance
- Section S7. Design of neotype co-firing multilayer shear-mode actuators
- Fig. S1. d34 mode piezoelectric metamaterials composed of various numbers of meta-atoms.
- Fig. S2. Specimen photographs of all seven kinds of piezoelectric metamaterials.
- Fig. S3. Test system for measuring effective displacement outputs of metamaterials.
- Fig. S4. Displacement responses to electric field of other five kinds of metamaterials.
- Fig. S5. Arrayed shear-mode metamaterials with in-plane arrangement way.
- Fig. S6. Preparation processes of neotype co-firing shear-mode multilayer actuator.
- Table S1. Schematic diagrams and definition formulas for calculating all effective piezoelectric coefficients.
Files in this Data Supplement:
