Ultra‐Stretchable Kirigami Piezo‐Metamaterials for Sensing Coupled Large Deformations

Abstract Mechanical metamaterials are known for their prominent mechanical characteristics such as programmable deformation that are due to periodic microstructures. Recent research trends have shifted to utilizing mechanical metamaterials as structural substrates to integrate with functional materials for advanced functionalities beyond mechanical, such as active sensing. This study reports on the ultra‐stretchable kirigami piezo‐metamaterials (KPM) for sensing coupled large deformations caused by in‐ and out‐of‐plane displacements using the lead zirconate titanate (PZT) and barium titanate (BaTiO3) composite films. The KPM are fabricated by uniformly compounding and polarizing piezoelectric particles (i.e., PZT and BaTiO3) in silicon rubber and structured by cutting the piezoelectric rubbery films into ligaments. Characterizes the electrical properties of the KPM and investigates the bistable mechanical response under the coupled large deformations with the stretching ratio up to 200% strains. Finally, the PZT KPM sensors are integrated into wireless sensing systems for the detection of vehicle tire bulge, and the non‐toxic BaTiO3 KPM are applied for human posture monitoring. The reported kirigami piezo‐metamaterials open an exciting venue for the control and manipulation of mechanically functional metamaterials for active sensing under complex deformation scenarios in many applications.


Note S1. Design and Fabrication Process of the piezoelectric rubber
As shown in the Fig S1, the piezoelectric rubber films were composed of PZT particles with a diameter of 1 μm (supplied by Quanzhou Qijin New Material and Technology Co., Ltd., China) and raw rubber mixed with 5 wt % curing agents, in a weight ratio of 4:1.The mixing was carried out using a roller milling machine with a diameter of 10 cm for about 1 hour until uniform distribution has been achieved.Subsequently, the blended piezoelectric composite was subjected to molding under a pressure of 10 MPa for a 24-hour period, resulting in varying thicknesses of 0.5 mm, 1 mm, and 2 mm, respectively.Considering that the elastic matrix tends to absorb oil and swell in oil bath, the resulting piezoelectric films were polarized using an external voltage of 60 kV/cm at 150 °C for 30 mins in air environment.With these steps, stretchable piezoelectric rubber films were successfully fabricated.After measuring, the piezoelectric constant d33 of PZT-mixed rubber is 23.4 pC/N.Specific process of PZT-mixed silicon rubber is demonstrated in Video S1.To study the effect of thickness , width  of ligaments, different parameters are designed.Table S1 presents the geometric properties of two kinds of kirigami structures, including the total length  1 , total width  2 , and thickness , width  of ligaments.

Note S3. More mechanical results of KPM sensors
For the C-KPM, the top three layers are symmetric in the vertical direction while the bottom layer is single.Therefore, the total axial deformation can be written as: where ∆  is the deformation of each layer.When analyzing the elongation of the ligaments, the deformation caused by the shear force is negligible.Since the external force is exerted to the C-KPM, the two ends of the elastic beams are fixed and the middle is stretched.The beams of the top three layers can be considered as the beams with fixed ends and displacement is applied to the end parts, while displacement is applied to the middle parts of the bottom ones.The total force is then divided into four equal parts for each beam in each layer, and therefore, the relationship between the displacement and force can be written as and Substituting Eqs.
(2) and (3) into Eq.(1) yields the relationship for the C-KPM as where the length of the ligaments   is related to the width  as For the R-KPM, different from the C-KPM, there are only three layers.Therefore, the total axial deformation can be written as As the external force is exerted to the structure, one end of the elastic beams is fixed and the other end deflects in bending.Since the deformation is evenly distributed to each layer, all beams are considered as the beams with fixed ends and axial displacement is applied to the end parts.The total force is divided into four equal parts for each beam in each layer.Therefore, the relationship between the displacement and force can be written as Substituting Eq. (7) into Eq.( 6) yields the relationship for the R-KPM as

Note S4. More mechanical results of KPM sensors
Figure S3 displays more results of Force-Displacement relationship of C-KPM and R-KPM with different design parameters.There exist similar variation trends for 3 designs of C-KPM and 3 designs of R-KPM, respectively.There are also deviations between experimental and numerical results.In simulation, the contacts between element faces are not considered.For C-KPM, the friction between adjacent ligaments (see Figure .2(c)) is distinct when the reaction force is small at the beginning loading process.With the increasing of deformation, the upper ligament parts are independent and there exists no contact with each other, so the numerical result agrees well with experimental result during the large deformation process.For R-KPM, the friction is only from one side of ligaments (see Figure .2(e)) and nearly half of C-KPM, on account of which these two results have better accordance.

Note S5. Numerical Simulations of the KPM sensors
The proposed kirigami structures combined with piezoelectric hyperelastic materials are simulated in ABAQUS.
The materials properties are listed in Table S2.The two structures were simulated with Tet mesh type due to the complex cutting.To carry out the deformation of the KPM sensors, the total face was separated into different parts by the datum face.The bottom annular parts of both structures were fixed and 90 mm displacement load was exerted to the top parts with constraint in x-y plane for C-KPM, while 190 mm displacement load was exerted to the top parts with no constraint in x-y plane for R-KPM.Taking the reality into account, the gravity is imposed to the total model.

Note S8. PZT proportion selection for the KPM
Figure S7 shows the influence of the PZT proportion on the coupling electromechanical performance of the piezoelectric film samples [35].Increasing the PZT particle weight ratio enhances the electrical performance of the piezoelectric samples while decreasing their mechanical properties.According to our preliminary testing, the optimal PZT particle weight ratio was found as 80 wt% since this configuration led to the optimal coupling electromechanical performance simultaneously.Satisfying the mechanical performance requirements (i.e., maximum stretching ratio: 200%), we selected the PZT proportion that the electrical performance reached its peak, ss shown in Figure S7.

Figure S7. The influence of PZT proportion on the coupling electromechanical performance of piezoelectric composite
materials [35].

Note S9. Comparation of the mechanoelectrical performance between the reported KPM sensors and the piezoelectric sensors
Figure 4(j) and Table S3 compare the mechanoelectrical performance (i.e., maximum stretching ratio and peak voltage) of our KPM sensors and previous reports.Our design makes progress in three-dimensional coupled in-and out-of-plane deformations monitoring of complex applications.Comparing with other plate-like sensors in the existing studies, the reported KPM sensors exhibit notable mechanical superiority, especially for monitoring coupled large deformations.Such advantage enhances their applicability in the scenarios requiring substantial deformations, which expands their potential applications.In addition, we have compared the deformation configurations of the KPM sensors with the existing piezoelectric sensors.The KPM sensors take advantage of the kirigami structures to significantly expand the stretching range and direction of the existing flexible PZT films.The peak voltage of the reported KPM is comparable to the existing materials, but the maximal stretching ratio of 200% is larger than the previously reported 150% [46].The distributions of the peak voltages under different displacement angles are depicted in Figure 4(i).

Note S10. Density measurement for three piezoelectric film samples
A MH-300A densitometer with a ±0.02 g/cm³ margin of error was selected to quantify the density of three piezoelectric film samples with the same length and thickness but different widths, as shown in Figures S8(a

Note S13. PE-protected PZT KPM
The potential toxic risk of the PZT KPM can be effectively mitigated by separating the contact surfaces using barrier materials.To this end, we used the ultrathin medical-graded polyethylene (PE) films to avoid the PZT KPM from directly contacting human skins, such that to provide necessary protection for human in healthcare applications.

Figure S1 .
Figure S1.The fabrication process of the piezoelectric rubber.

Figure S2 .
Figure S2.The design mechanism of the KPM sensors.
The boundary and loading conditions are provided in Fig S4.

Fig
Fig. S5 demonstrates the cyclic loading and unloading tests of KPM structures (set  = 2 ,  = 5  as example), which shows good stability from mechanical perspective.Additionally, the area difference in the graph represents the dissipated energy during the loading and unloading process.

Figure S5 .
Figure S5.Force-displacement relationship of the C-KPM subjected to the cyclic loading with 20 cycles.

Figure S6 .
Figure S6.Field testing setup of KPM sensors glued to the surface of the tire to monitor the state of the tire.
) and (b).The density and mass distributions of the three samples are shown in FigureS8(c).Two samples had the same density of 3.495 g/cm³ and the third sample has the density of 3.465 g/cm³.These results indicate the uniform density distribution of the piezoelectric film samples with density differences below 1%.The density measurement procedures for the piezoelectric film samples are observed in Supporting Video S7.

Figure S8 .
Figure S8.Density measurement for three PZT piezoelectric film samples.(a) Three piezoelectric film samples with the length and thickness but different widths.(b) Photographs of the measuring instruments and three samples.(c) Density and mass distributions of the three piezoelectric film samples.

Figure
Figure S9.X-ray diffraction comparison and high-resolution SEM images of the PZT rubbery films.(a) X-ray diffraction (XRD) comparison between three positions in a KPM sample.(b) Content of substance components comparison between three positions in a KPM sample.(c) High-resolution SEM images of the PZT rubbery films.

Figure S10 .
Figure S10.Illustration of stretchability of the KPM.(a) Schematic illustrations of the stretching (i.e., out-of-plane deformation) of the R-KPM.(b) Force-displacement relationship of the R-KPM under the out-of-plane loading displacement of 20 cm.
Figure S11(a) demonstrates the PZT KPM with the adhesive PE films on the top and bottom surfaces in the application of human wrist posture monitoring.The PZT KPM are sandwiched between the two layers of the PE films and bonded on the wrist, thereby ensuring the deformations together with the human wrist while preventing direct skin contacts.Figure S11(b) shows the field-testing images of the PE-protected PZT KPM sensors attached to the human wrist under different postures (i.e., bending and releasing states).

Figure S11 .
Figure S11.PE-protected PZT KPM.(a) Separation of the toxic PZT KPM by adhesive PE films for human wrist posture monitoring.(b) Field-testing images of the PE-protected PZT KPM sensors attached to the human wrist under different postures (i.e., bending and releasing states).

Table S2 .
material properties of piezoelectric silicon rubber.
S4. Load and boundary conditions of the KPM sensors.Note S6.

Table S3 .
Comparation of the structural design, material composition, and mechanoelectrical performance between the reported KPM sensors and the existing piezoelectric sensors.