Topological designs
Many thin film resistive strain sensors are based on a continuous, rectangular geometry, which was employed as the Non-Patterned control set in this study (Fig. 1a). Since the aim of this study was to manipulate thin film strain sensing properties when the material system remained unchanged, different topological designs were proposed. By varying thin film topologies, the tension-induced stress and strain distributions in the patterned material system could be altered and controlled. Here, two main categories of different topologies were designed, namely, stress-concentrating and stress-releasing topologies, which are presented in Figs. 1b-d and Figs. 1e-f, respectively.
First, the stress-concentrating designs started with the creation of a grid-like pattern in lieu of a continuous rectangular geometry (i.e., the Grid as shown in Fig. 1b and Supplementary Fig. 1a). Second, the introduction of stress concentrations was based on the inhomogeneous stress distribution in the commonly used dog-bone test coupon. It is well-known that a dog-bone-shaped structure pulled in tension would result in concentrated stresses and strains in its tapered center region. Thus, the vertical elements of the grid design in Fig. 1b were substituted with dog-bone elements to purposely introduce inhomogeneity to the structure (i.e., considering that tension is applied along the vertical direction), as shown in Fig. 1c (i.e., the Dog-Bone). The detailed dimensions of the dog-bone unit are illustrated in Supplementary Figs. 1b–c. In addition, the horizontal elements were replaced with an inverse dog-bone shape to combat Poisson’s effect. Last, to further enhance stress concentrations, a hierarchical design was employed, where the shape of the entire grid was modeled after a dog-bone structure (Fig. 1d and Supplementary Figs. 1d-f). This design also entailed the incorporation of smaller dog-bone units as the vertical elements, as is shown in Fig. 1d, which is herein referred to as the Hierarchical Dog-Bone.
On the other hand, the stress releasing topological designs were inspired by a Japanese paper cutting artform called Kirigami. The Kirigami-based structure allows for enhanced elastic softening and large deformations of an otherwise rigid or non-stretchable substrate material28. The Kirigami design shown in Fig. 1e and Supplementary Fig. 1g included a periodic array of horizontal cuts (Supplementary Fig. 1i) that releases stresses when the entire structure is subjected to vertically applied tension. In addition, this study also introduced a Modified Kirigami structure (Fig. 1f and Supplementary Fig. 1h), which has additional curved corner cuts on both ends of the horizontal cuts (Supplementary Fig. 1i) so as to further release stress concentrations.
Numerical Analysis Of Stress Fields
FE modeling using the Solid Mechanics Module of COMSOL Multiphysics was performed to verify that the various topological designs in Fig. 1 could effectively concentrate or release tension-induced stresses in the films. Figure 2 shows the von Mises stress fields in thin films of different topologies when subjected to a 1% tensile strain applied in the vertical direction. Figures 2a-d indicate that stresses were concentrated in the inhomogeneous vertical elements, and the overall magnitude of stress (in the vertical elements of the dog-bone shape patterns) was increased due to inhomogeneity of the pattern. In addition, the Hierarchical Dog-Bone (Fig. 2d) possessed the most dominant stress concentrations, as well as the highest stress magnitudes in the corresponding inhomogeneous elements. In other words, stress concentrations could be achieved by introducing inhomogeneity in the material topology, and such stress concentrating effect could be enhanced using hierarchical designs.
On the contrary, Kirigami structures were expected to relieve stress concentrations. Figures 2e and 2f show the stress distributions in the Kirigami and Modified Kirigami designs, respectively. One can see that the stress magnitudes in these topologies were significantly lower than the Non-Patterned control set, as well as versus those of the stress-concentrating topologies. In particular, the Modified Kirigami design (Fig. 2f) was characterized by an even lower stress distribution than the conventional Kirigami structure in Fig. 2e, which was achieved by purposely introducing additional corner cuts at the ends of the horizontal cuts. Therefore, the FE modeling results indicated that the designed hierarchical inhomogeneous topologies led to enhanced stress concentrations, whereas cuts in the film or Kirigami-based topologies effectively reduced stress distribution and stress concentrations.
Strain Sensing Characterization Of Nanocomposite Thin Films
Nanocomposite thin films of different topological designs and experimentally tested to validate how the stress-concentrating and stress-releasing designs affected bulk film piezoresistivity. Two different nanocomposite material systems, including GNS-EC and CNT-latex, were fabricated to form the aforementioned topologies subjected to strain sensing characterization tests.
Figure 3a shows the representative normalized change in resistance ΔRn time histories of the control set and patterned GNS-EC thin films when they were subjected to tensile cyclic strains. Among the different topologies, it can be seen that the ΔRn time histories of the Non-Patterned (control set), Grid, Dog-Bone Grid, and Hierarchical Dog-Bone followed closely with the applied tensile cyclic strain pattern in a stable and repeatable manner. In addition, the thin films patterned with stress-concentrating designs exhibited larger normalized changes in resistance (i.e., were more sensitive to strains) than the homogeneous control set.
To better compare the strain sensitivities or gage factors (GFs) of the different topology GNS-EC nanocomposite thin films, Fig. 3b plots ΔRn as a function of applied strains (Δε). Here, GF is defined according to Equation 1:
$$GF=\frac{\varDelta {R}_{n}}{\varDelta \epsilon }$$
1
Although the strain sensing response of the grid structures were polynomial, as is shown in Fig. 3b, linear least-squares best-fit lines were fitted to the data corresponding to ≥ 0.3% applied strains. Then, the slopes of the fitted linear lines were computed as an estimate of thin film GFs (according to Equation 1). It can be seen from Fig. 3b that the linear approximation was able to sufficiently characterize the changing trends of ΔRn for the various nanocomposite topologies tested. To be specific, the GFs of the Grid, Dog-Bone Grid, and Hierarchical Dog-Bone topologies were calculated to be ~ 38, 41, and 60, respectively. This indicated that the bulk film GF of the GNS-EC strain sensors could be effectively increased by leveraging the inhomogeneous topology-induced stress concentrations in the material system. In addition, higher levels of hierarchical inhomogeneity led to more significant enhancements in strain sensitivity. These results imply that high-sensitivity sensors could be developed solely based on designing the material’s topology. It was hypothesized that the piezoresistivity of GNS-EC thin films mainly stem from deformation- and strain-induced disturbances to the percolated and conductive GNS network of the nanocomposite. In particular, applied tensile strains would induce separations between individual or small bundles of GNS to decrease the total number of GNS-to-GNS contacts, thereby reducing the number of overall electrical current conducting pathways in the nanocomposites and thus leading to higher bulk film resistance. Based on this hypothesis, this study focused on manipulating the stress distribution in nanocomposite thin films and used this as a mechanism for controlling their bulk film strain sensitivity. For instance, when higher strain sensitivity is desired, significant disturbances in the GNS-conducting pathways could be achieved by purposefully incorporating stress and strain concentrations in the nanocomposite.
On the other hand, based on the same hypothesis, the Kirigami-based topologies were designed to release stress/strain concentrations in the nanocomposites so as to reduce disturbances to the percolated GNS networks and to minimize strain sensitivity. From Figs. 3a and 3b, one can observe that the Kirigami-based nanocomposite specimens exhibited significantly lower strain sensing response. The suppressed strain sensitivity was especially obvious for the Modified Kirigami topology sample set, whose GF was found to be ~ 0.48 (Fig. 3b). These results suggested that the global strain sensing performance of piezoresistive nanocomposite thin films could be efficiently suppressed by releasing stresses in the material system and by preserving their nanostructure during large deformations. In other words, the stress-releasing topologies (i.e., Kirigami-based structures in this study) are promising candidates for decoupling sensing signals induced by strains/deformation from the primary desirable measurand.
Overall, Fig. 3c summarizes the normalized difference in GFs (ΔGFn = (GFi−GF0)/GF0) obtained by the proposed topological designs as compared to the Non-Patterned control set for the GNS-EC nanocomposites. Here, GFi represents the GF values of each pattern, while GF0 is that of the Non-Patterned sample set (~ 40). It was found that, based on the same GNS-EC material system, a topological design strategy could achieve a remarkably expanded spectrum (-99% to +50%) of strain sensing performance. This indicates that the proposed topological design approach could be potentially leveraged to strategically manipulate and design the bulk material’s piezoresistivity in a predictable and controllable manner.
This study also experimentally characterized the strain sensing performance of patterned CNT-latex nanocomposite thin films to further validate the effectiveness and applicability of this topological design strategy. The representative ΔRn time histories of the CNT-latex specimens from the strain sensing tests, as well as ΔRn as a function of Δε, are shown in Supplementary Figs. 2a and 2b, respectively. In addition, Fig. 3d summarizes the normalized difference in GFs (i.e., ΔGFn) obtained by the proposed topological designs as compared to the Non-Patterned control set of CNT-latex specimens. One can observe that the stress-concentrating topologies enhanced the strain sensitivity of the CNT-latex nanocomposites by ~ 70% (i.e., Hierarchical Dog-Bone), while the stress-releasing structures suppressed piezoresistivity by ~ 95% (i.e., Modified Kirigami). These results further demonstrated that the topological design-based approach could consistently manipulate different piezoresistive nanocomposite material systems, paving ways for next-generation multifunctional materials development and strategies for engineering specific material properties.
Numerical Analysis Of Electromechanical Response
While the experimental tests validated tuning of bulk material strain sensitivity, design would require a numerical model that considered the electromechanical properties of the material system. Therefore, two different material models were developed in this work, which included a calibrated linear piezoresistive material model and a percolated inhomogeneous material model (modeling details are described in Supplementary Information). Since the linear piezoresistive material model was unable to simulate the nonlinear behavior observed from experimental data (Fig. 3b and Supplementary Fig. 2b), this section mainly focuses on the performance of the percolated material models.
It was hypothesized that the experimentally observed nanocomposite strain sensing response mainly stemmed from mechanical loading-induced disturbances to its distribution of electrical defects. To be specific, increasingly applied tension could generate more electrical defects in the material system, which would correspondingly increase bulk electrical resistance of the nanocomposite. Such defects were introduced to the percolated inhomogeneous model by seeding the material model with randomly distributed electrical defects (i.e., low electrical conductivity). These randomly distributed inhomogeneous features (i.e., electrical defects) would propagate according to the externally applied mechanical deformations (e.g., tension) and result in an increase in its electrical resistance.
Therefore, the percolated inhomogeneous model considered a 3D domain of interest with dimensions of 40×40×0.1 mm3 (i.e., slightly larger than the dimensions of the designed topologies). A randomized statistical dataset was first generated to define the initial set of electrical defects (Supplementary Information). Figure 4a shows the synthesized random data distributed in the 3D domain, and Fig. 4b shows five slices on the y-z plane of the thin slab to expose the data distribution inside of the slab. The randomized dataset was attributed to each patterned material model by truncating it from the same 3D thin slab.
For the GNS-EC nanocomposite system, the percolated material model was first calibrated based on the Non-Patterned control set. Figure 4c shows the spatial distribution of electric potential, overlapped with isosurfaces of electric potential in the Non-Patterned material model, when it was subjected to 1% tensile strain along the y-axis. It can be seen that electric potential was nonuniformly distributed, indicating that inhomogeneous electrical conductivity distribution was successfully introduced to the material model. In Fig. 4d, the normalized change in voltage ΔVn of the calibrated Non-Patterned control set was plotted as a function of applied strains and overlaid with the corresponding experimentally measured ΔRn results, as well as the ΔVn computed using the linear piezoresistive model, for comparison. Overall, the inhomogeneous material model not only introduced nonlinearity to the simulated strain response but also more accurately characterized the strain sensitivity of the GNS-EC nanocomposites than the linear model. Furthermore, Figs. 4e and 4f show the electrical conductivity distributions of the calibrated Non-Patterned material model when it was subjected to 0.5% and 1% tensile strains, respectively. Fig. 4g and 4h also show the internal conductivity distributions corresponding to Figs. 4e and 4f, respectively. The electrical defects clearly propagated in the material when subjected to larger strains.
Then, the calibrated material model was implemented to simulate the electromechanical responses of the other patterned material models. Figures 5a to 5d demonstrate the electrical defects distributions and development in the Hierarchical Dog-Bone and Modified Kirigami material models when they were subjected to 0.2% and 1% strains, respectively. The electrical defect distributions of the Grid, Dog-Bone Grid, and Kirigami are shown in Supplementary Figs. 4 to 6, respectively. Based on Figs. 5a to 5d and Supplementary Figs. 4 to 6, it can be observed that electrical defects mainly formed and propagated at the stress-concentrating regions. For the Kirigami topologies, since stress was effectively released from the material, the electrical defects barely developed even at 1% strain. In addition, Fig. 5e overlays the simulated electromechanical responses of all the patterned material models as functions of applied strains. The proposed inhomogeneous material models agreed well with the experimental strain sensing test results, where both showed that the stress-concentrating topologies could enhance nanocomposites thin film piezoresistivity, while the stress-releasing topologies could significantly suppress their strain sensing responses.