Designing electromechanical metamaterial with full nonzero piezoelectric coefficients

Abstract

Designing topological and geometrical structures with extended unnatural parameters (negative, near-zero, ultrahigh, or tunable) and counterintuitive properties is a big challenge in the field of metamaterials, especially for relatively unexplored materials with multiphysics coupling effects. For natural piezoelectric ceramics, only five nonzero elements in the piezoelectric matrix exist, which has impeded the design and application of piezoelectric devices for decades. Here, we introduce a methodology, inspired by quasi-symmetry breaking, realizing artificial anisotropy by metamaterial design to excite all the nonzero elements in contrast to zero values in natural materials. By elaborately programming topological structures and geometrical dimensions of the unit elements, we demonstrate, theoretically and experimentally, that tunable nonzero or ultrahigh values of overall effective piezoelectric coefficients can be obtained. While this work focuses on generating piezoelectric parameters of ceramics, the design principle should be inspirational to create unnatural apparent properties of other multiphysics coupling metamaterials.

Fig. 1. Piezoelectric strain matrix with full nonzero elements d_ij 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).