Embedded Pressure Sensing Metamaterials Using TPU-Graphene Composites and Additive Manufacturing

Disabilities impacting mobility are a global concern requiring gait rehabilitation, where monitoring foot pressure distribution is fundamental. Wearable systems provide an alternative to stationary equipment eliminating space limitations. However, wearable sensors present challenges in the calibration, sensitivity, and human–sensor interface, requiring application-specific sensors. This study aimed to develop wearable sensors, where the structural and material properties can characterize the sensitivity and range of measurement during the design phase. We developed wearable piezoresistive sensors using additive manufacturing (AM) to create mechanical metamaterials with embedded pressure-sensing capabilities. Three structural designs were developed for different measuring ranges (0–50 N, 0–100 N, and 0–150 N) using body-centered cubic (BCC) lattices constructed via pyramid unit cells. In addition, two graphene infusion processes were evaluated. We analyzed the influence of structural dimensions and the graphene infusion process on the piezoresistive response of the sensors. The measuring range was affected mainly by tunable structural dimensions, while the infusion process influenced the piezoresistive sensitivity and the linear response. The outcomes in characterizing the piezoresistive sensors based on structural and material properties could allow the development of wearables with embedded pressure sensing with a predictive response solely based on design parameters using AM and graphene inks.

repetitive measurement of applied strain. Piezoresistive sensors can be fabricated using a wide range of flexible substrates coated with conductive materials [23], [25], [26]. Over the last decade, discoveries in the applications of graphene in sensing electronics and a decrease in exfoliation costs have resulted in the development of wearable pressure sensors using graphene composites [27], [28], [29]. However, the development of piezoresistive pressure sensors still presents design challenges affecting their use across applications.

A. Additively Manufactured Sensors
Additive manufacturing (AM) technologies can solve some of the main challenges present in current wearable sensors involving sensitivity, stretchability, linearity, scalability, durability, and cost-effectiveness [30], [31]. The formulation of graphene inks, polymer composites, and conductive inks has been successfully introduced in the AM process to develop wearable sensors [32] using fuse deposition modeling (FDM) [33], [34], digital light processing (DLP), and hybrid photopolymerization techniques [35]. Furthermore, selective laser sintering (SLS) enables the creation of microstructure polymer matrices with suitable mechanical and piezoresistive properties in pressure sensors, presenting the potential for a customized sensing response [36]. Although AM can bring further prospects to the fabrication of wearable sensors, there are limitations intrinsic to the manufacturing methods related to scalability and cost-effectiveness. Photopolymerization techniques [e.g., DLP and stereolithography (SLA)] have been focused on replicating the standard methods of fabricating sensors using substrate elastomers, such as polydimethylsiloxane (PDMS) or polyethylene terephthalate (PET) substrates [37], [38], and replacing them with photocurable resins [35]. FDM presents resolution limitations for fabricating sensitive microstructures [23], [33]. An unprecedented approach is needed to maximize the benefits of AM technologies and elastomer conductive composites. The challenges regarding embedding, durability, characterization, calibration, and cross-application could be alleviated by exploiting AM technologies and carbon-based sustainable conductive materials; embedding pressure sensing using mechanical metamaterials.

B. Mechanical Metamaterial Sensors
Mechanical Metamaterials are man-made materials that obtain their effective properties mainly by architecture rather than composition. Metamaterials can be engineered to have piezoresistive properties using semiconductive composites [23]. They can modify their physical behavior due to tunable hierarchical architectures at the micro-and nanoscale levels [39]. The relationship between the compressive strain distribution and the piezoresistive sensitivity can be used to define the optimal geometry of the sensor [36]. Intricate lattices have been explored to create flexible compressive structures in assembled AM pressure nanogenerators [40]. AM allows the fabrication of macro-and microlattice structures with configurable porosity and stiffness. Piezoresistive properties can be conferred to the AM structure using graphene, creating metamaterial composites. Although calibration is required for accurate measures, characterizing the piezoresistive behavior based on design parameters could help alleviate the calibration process and predict the expected sensitivity and range of measurement. Previous studies have shown that characterizing the piezoresistive behavior and the sensitivity can help achieve customized stretchable and compressive sensors [29], [41].

C. Purpose of the Study: Embedded Sensing
The materials used to develop wearable sensors highly depend on the application requirements, which define the sensors' dimensions, geometry, sensitivity, and bandwidth. Introducing AM metamaterials to embed sensing inside wearable devices could increase customization, use across various applications, and help remove the human-sensor interface. Due to the relationship between strain and stress, the piezoresistive sensing behavior can be controlled by modifying the structural stiffness of the material to create sensors with custom measurement ranges. The characterization of material and design properties (piezoresistivity and structural stiffness) could lead to a predictive response following specific sensitivity and characteristics that match the application's needs. The parametrization of lattices enables the modification of compressive stiffness, resulting in different sensitivities in piezoresistive pressure sensors [41]. A deliberate methodology is needed to achieve extensive characterization, considering the design aspects and controlling the manufacturing process parameters.
This study aims to develop wearable piezoresistive sensors using mechanical metamaterials and AM, where the structural and material properties define the sensitivity and range of measurement. In addition, parametric lattice structures are used to provide stiffness configuration capabilities.

II. PARAMETRIC DESIGN AND EXPERIMENTAL TESTING A. Structural Lattice Configuration
We parametrically designed mechanical metamaterial sensors to investigate the effects of changes in the compressive stiffness and piezoresistive properties in the range of measure and sensitivity. Three sensor designs were developed using 3-D pyramid lattice structures to measure different compressive force ranges based on crystal microstructures [42]. A lattice formed by pyramid body-centered cubic (BCC) model with identical unit cell orientation was selected to achieve uniform deformation along the range of measure and minimize the nonlinear effects of the piezoresistive behavior of the sensors [ Fig. 1(a)]. The dimensions of the sensors and compressive forces were based on the range from wearable sensors used in the monitoring of foot vertical ground reaction forces (VGRF) during gait [10], [11]. The three structural designs, A, B, and C, were developed to have different ranges of measurement from 0-50 N, 0-100 N, and 0-150 N, respectively. Finite element simulations were performed to analyze the structural design sensitivity and mechanical compressive saturation at the corresponding limit forces based on the strain concentration, which relates to the sensitivity of SLS flexible piezoresistive sensors [36] [ Fig. 1(b)]. Structural saturation was defined as the mechanical compressive saturation when the struts of the intricated lattice underwent contact with each other.

B. Fabrication and Graphene Infusion
The sensors were manufactured in two separate stages. First, the samples were printed using an SLS 3-D printer EOS Formiga P100 (EOS, Krailling, Germany) in thermoplastic polyurethane (TPU) Ultrasint 88 A material (BASF SE, Ludwigshafen, Germany). Second, the samples underwent an ultrasonic bath to remove the remaining powder inside the lattice and were dried to prepare them for the infusion process. Third, each sample was immersed in a graphene-ethanol ink solution. The graphene used was CamGraph (Cambridge Nanosystems, U.K.), with a carbon purity >99.5% and an average lateral size of 0.15 µm. Two graphene-ink solutions (0.5 and 2.5 mg·mL −1 ) were prepared by sonicating the graphene in ethanol for 10 min based on the graphene concentrations used in previous studies [28], [43]. The TPU samples were separated into two groups that underwent two different infusion processes to see the effects on the piezoresistive behavior of the designed sensors [ Fig. 1(c)]: 1) the samples from the first group were immersed in a single infusion in a solution with a concentration of 2.5 mg·mL −1 and 2) the samples from the second group went through two consecutive infusions of 0.5 and 2.5 mg·mL −1 concentrations, respectively. The sensors were dried using a vacuum oven after each infusion process at 40 • C for 2 h.

C. Experimental Testing and Characterization
We tested the compressive stiffness of the structural designs using an Instron Series 5800 testing system (MTS Systems Corporation, Montana, USA) to measure the force and displacement to validate the ranges of measurement determined from the strain concentration results of the finite element simulations. Two compression cycles at a compression rate of 4 and 30 mm·min −1 were tested to analyze the influence of the loading rate. The final dimensions of the sensors were measured using a caliper to obtain the actual measurements of the samples. The piezoresistive response of the sensors was obtained by measuring the electrical resistance between the top and bottom layers during the compression cycle. A set of two samples were used for each of the six sensor configurations (structural design and graphene infusion combinations). A total of four consecutive compression cycles were performed. The mean and standard deviation values were calculated to analyze the results. One of the double infusion samples produced electrical resistance changes more significant than one and a half the interquartile range of the sample group and was discarded as an outlier sample. The changes in the electrical resistance (resistivity) across the sensor from the top to the bottom surface were expressed with respect to the intrinsic resistance (R 0 ) of the samples without any applied compressive load. The piezoresistive response of the sensors was analyzed against the applied force and the compressive strain and represented as percentage values.
The piezoresistive sensitivity is the main factor to characterize the piezoresistive behavior of sensors, which is analyzed by the effects of mechanical stresses and strain in the electrical resistance fluctuations [44]. The sensitivity was analyzed using the gauge factor (GF) calculated by (1). The calculation of the GF is defined as the ratio between the relative change of resistance ( R) with respect to the intrinsic resistance (R 0 ) of the sensor and the compressive strain along the direction of the applied force (ε). The compressive strain is calculated as the decrease in height ( L) with respect to Authorized licensed use limited to the terms of the applicable license agreement with IEEE. Restrictions apply.  I  DIMENSIONS AND TOLERANCES OF THE CAD DESIGNS AND THE  SLS-PRINTED SAMPLES COATED WITH GRAPHENE FOR THE  DEVELOPED  The gradient of the GF is represented as the derivative of the sensitivity function, indicating the gradient sensitivity for the compression range [36], [45]. The sensitivity function was obtained for each sensor through polynomial regression fit of the ( R/R 0 ) data. The sensitivity functions were analyzed to determine the sensing ranges and their corresponding GFs Compression tests were performed from 0 to 100 N following the load ranges from force sensing resistors (FSR) and graphene pressure sensors used in sensitive insoles that monitor the foot pressure distribution [10], [46]. In addition, we carried out a microstructural analysis using a scanning electron microscope (SEM) to evaluate the graphene deposition over the infused samples. The images of the infused samples were taken after the vacuum drying process and were used to compare the graphene concentration on the samples' top and bottom surfaces.

III. RESULTS AND DISCUSSION
The effects of the structural properties and the infusion process were observed in the compressive stiffness and piezoresistivity results of the different designs, resulting in changes in the piezoresistive response. The dimensions and tolerances of the design and produced samples are described in Table I. Observing the compressive stiffness results (Fig. 2), the saturation limits from the finite element simulations (Fig. 1) were supported by the stiffness results from the compressive testing for the three designs, A-C.

A. Compressive Stiffness
The maximum compliance was found for the design A lattice structure ( Fig. 2) with actual measurements of 1.21 ± 0.07 mm for the strut diameter and 0.94 ± 0.07 mm for the thickness of the top and bottom surfaces. The mean differences in the samples' structure between designs C and A were +0.24 ± 0.12 mm for the strut diameter and +0.38 ± 0.11 mm for the top and bottom thickness, resulting in an increased mean compressive stiffness ratio of design C   Fig. 2(a)]. Despite the large differences in the thickness of the top/bottom surface, the stiffness results showed minor differences between designs B and C from 0% to 15% strain [ Fig. 2(d)]. Although designs B and C showed similar stiffness curves from 0 to 71 N, the characteristics of the TPU lattice structures at the end of the compressive range produced convex trajectories, increasing the slope of the compressive stiffness. This effect, which has been observed in additively manufactured supportless lattice structures [47], resulted in a higher stiffness of design B, with a lower compressive strain at 100 N of 17.82% compared to design C, with a strain of 19.58% for the same force.
The results from designs A and C indicate that microdifferences in the strut diameter and top/bottom surface thickness result in large differences in the compressive stiffness of miniature TPU additively manufactured structures. This is supported by previous studies, which have found that lattice structures display a power law relationship dependent on the structure's relative density and compressive properties [48], [49], [50]. The three designs exhibited hysteresis during the loading and unloading cycle, a behavior observed in TPU auxetic lattice structures fabricated using SLS [51], and in fused filament fabricated capacitive pressure sensors for plantar monitoring [52]. Furthermore, the compressive velocity did not affect the strain response, where 4 and 30 mm·min −1 compressive velocities produced similar mean trajectories [ Fig. 2(d)]. The compression curves from a previous study using TPU-graphene parametric structures in piezoresistive sensors showed comparable compressive stiffness curves from the range of forces 0-100 N and 0-150 N, with strain results ranging from 0% to ∼25% [36].

B. Graphene Concentration
The graphene concentration results from the SEM images show the microstructure of the uncoated and coated surfaces (Fig. 3). The structure of the sensors has an intricate lattice of solid core struts [ Fig. 3(d)], which allowed the graphene coating to deposit over the external surfaces of the lattice struts. The SEM images also show the morphology of the samples due to SLS AM, which created a rough and porous surface that facilitated the adhesion of graphene ink during the infusion process. The comparison of the uncoated and coated surfaces [ Fig. 3(a)] showed a clear distinction through the reflection of high-energy electrons from the deposition of the graphene. Although double infusion samples were hypothesized to have stacked more graphene over the sensors' surface, the single infusion and double infusion samples had similar reflection intensity at areas with deposited graphene [ Fig. 3(b) and (c)]. This may result from the common final concentration of 2.5 mg·mL −1 for both the single and double infusion processes.

C. Stiffness and Graphene Infusion Effects in Piezoresistivity
The design with the highest compressive compliance (design A) presented minor variations of the electrical resistance for the designed range of measurement [0-50 N (0%-27% strain)] in both single and double infusion samples. For the single infusion of design A, the mean electrical resistance of the sensor decreased to −0.17 ± 0.12 with respect to the initial resistance when compressed from 0 to 9.6 ± 5.6 N [ Fig. 4(a)]. The resistance decreased progressively for the double infusion, reaching a mean of −0.17 ± 0.12 when compressed from 0 to 14.8 ± 10.8 N [ Fig. 4(d)]. The piezoresistivity of design A was very similar for both single and double infusion for the designed force range (0-50 N) independently of the infusion process. However, the sensitivity of design A for the double infusion was found to have a higher force range of measurement than the single infusion, reaching 14.8 N (7.9% strain) before the expected mechanical compressive saturation. Both infusions had a similar response from 0 to 10 N (0%-6% strain) and similar behavior over the targeted force range. An increase of the compression force beyond this point did not result in variations of the electrical resistance until reaching the mechanical saturation limit zone at 55.7 ± 25.6 N [ Fig. 4(a)] for the single infusion samples and at 44.1 ± 7 N for the double infusion samples [ Fig. 4(d)].
After reaching the mechanical compressive saturation of design A samples, the electrical resistance increased for the single infusion samples to a mean value of 0.013 ± 0.014. In contrast, the resistance dropped abruptly for the double infusion samples to a mean value of −0.56 ± 0.36. The results indicate the influence of the double infusion process for design A. The large electrical resistance changes occurring after reaching the mechanical saturation limit could have occurred due to the increased contact of the lattice struts caused by mechanical compressive saturation and the additional graphene infusion. Although double infusion for design A showed higher sensitivity than single infusion and an extended range of measurement beyond the designed mechanical saturation, the large variability between samples indicated by the standard deviation limits the sensitivity of design A with low forces ranging from 0 to 15 N. Furthermore, the different piezoresistive response curves observed from 0 to 50 N compared to 50-100 N indicates the unsuitability of design A lattice structural dimensions for the designed measurement range from 0 to 50 N [ Fig. 4(d)]. However, the double infusion process suggests the potential suitability of the design for a measurement range of higher forces.
The sensitivity of design B for the range of measure 0-100 N exhibited a mean linear response with a maximum resistance decrease of −0.30 ± 0.19 for the single infusion at 100 N [ Fig. 4(b)]. Conversely, the double infusion decreased up to −0.25 ± 0.21 at 59 N. Both infusion processes resulted in similar maximum change in resistance values from 0 to 50 N; however, for the double infusion, the piezoresistive saturation was reached at 59 N, with no further changes in the electrical resistance until the designed compressive limit of 100 N. The results from the double infusion samples response were comparable to the double infusion of design A, with an electrical saturation plateau after 60 N. The single infusion for design B displayed a linear piezoresistive response for the entire range of measurement. Despite this, design B displayed variability and large standard deviations for both infusions. The structural design approach to reduce the contact surface resulted in an asymmetry of the geometry, which may have affected the structural stability during compression, affecting the repeatability and linearity of the response.
Lastly, for design C, the single infusion samples' response followed an exponential decay without experiencing electrical saturation along the measuring range. The highest sensitivity was found from 0 to 30 N and reached a mean decrease in resistance of −0.71 ± 0.09 at 100 N [ Fig. 4(c)]. The piezoresistive response (force/electrical resistance change) followed an exponential decay response; this is comparable to the findings in previous studies using force sensor resistors to measure the foot contact forces during gait [28], [53], indicating the potential of design C and single infusion combination as a wearable sensor to measure VGRF. The double infusion samples produced a linear response for the designed range of measurement, with a mean decrease of −0.48 ± 0.07 at 100 N [ Fig. 4(f)]. One of the double infusion samples exhibited more sensitivity from 0 to 30 N (Fig. 4(f) [ii]), similar to the piezoresistive response curve of the single infusion samples for the same range of measurement. These results show that the infusion process influenced the piezoresistive sensitivity ranges. A single infusion of the samples in graphene led to substantially greater sensitivity at lower forces, while a double infusion produced a linear response through the measuring range. Furthermore, design C samples resulted in a piezoresistive behavior with high repeatability within each sample for both single and double infusion [ Fig. 4(c) and (f)].
The changes in the lattice structure greatly impacted the sensors' stiffness and the piezoresistive response independently of the infusion process. The lattice structure of designs A and C and the compression surface are the same, except for the strut diameter and top/bottom layer thickness. Design A increased the strut diameter by 0.24 ± 0.12 mm and by 0.38 ± 0.11 mm in the top/bottom layer thickness compared to design C. However, the mechanical and piezoresistive response results reflected major differences in the piezoresistive sensitivity. The results show the effects of microscale changes in the structural design parameters on the sensitivity and repeatability of the measures, highlighting the importance of tolerances in the AM of piezoresistive sensors.

D. Piezoresistive Sensitivity
The piezoresistive sensitivity function of each sensor was obtained through polynomial regression fit of the piezoresistive  Table II for the different designs and infusions. For design A, single infusion, the piezoresistive sensitivity resulted in a GF of −11 for the strain range from 0% to 10% and −31 for the range from 10% to 30%, while the double infusion resulted in a GF of −2 and 2 for the corresponding ranges, therefore displaying a low piezoresistive sensitivity. Design A single infusion increased the GF from the sensing strain range from 10% to 30%; however, after mechanical compressive saturation (>30% strain), the samples did not experience changes in the electrical resistance. Design B also exhibited low sensitivity for the sensing range from 0% to 10% for both single and double infusion, with a GF of −3 and 0, respectively. For the strain range from 10% to 18%, the single infusion GF was 9 and 29 for the double infusion.
Positive piezoresistivity (GF > 0) is common in compressive sensors caused by a decrease in the electrical resistance to the applied force; meanwhile, an increase in the resistivity (GF < 0) is more common in tensile sensors [54]. The results from design A indicate a resistance increase and negative GFs for the compressive sensing ranges for both the single and double infusion for the designed range of measurement (0-50 N). This behavior shows a resistive effect rather than a piezoresistive, which could have been due to dimensional changes of the sensor, increasing strain in directions different to the resistivity direction from the top to the bottom surface.
Among the different sensor designs and graphene infusion combinations, design C single infusion resulted in the highest sensitivity for the compressive sensing ranges (Fig. 5). The results show the high sensitivity of design C single infusion, where the sensitivity function was defined by a sixth-order polynomial regression fit (R 2 = 0.998) in (3). The derivative of the sensitivity function resulted in the GF gradient determined by (4). A GF of 67 was found for the sensing range from 0% to 7% and 282 for the 7%-20% range. For the double infusion, the GF for the sensing range was −3. Although the double infusion of design C produced a linear response, the piezoresistive sensitivity defined by the GF was found to be low and negative The sensitivity of SLS-printed TPU-graphene piezoresistive compression sensors has shown in a previous study a maximum GF of −1.74 using a Schwarz structure [36]. Graphene textile piezoresistive strain sensors have reported maximum sensitivities with a GF of 498 but require larger sensing strain ranges of 293% [55]. CNT/TPU nanocomposites piezoresistive sensors have demonstrated a high linearity response with a GF = 1.42 for pressure ranges up to 40 kPa [56]. However, for the range of measurement forces required for gait monitoring of the VGRF and the surface of the sensing area, our sensors can measure up to 200 kPa. Furthermore, our sensor design C with single infusion improved the GF exhibiting high sensitivity, with a maximum GF = 420 and a maximum compressive sensing range of 20% strain from 0 to 100 N. The small compressive strain range of 20% provides a promising application of compression sensors for gait monitoring of the foot contact forces, providing high sensitivity without requiring large displacements, which could allow their installation in shoe soles and insoles.
The single infusion resulted in higher sensitivity for design C than the double infusion, indicating the infusion process's effects on the piezoresistive sensitivity for the same lattice structural design. The low sensitivity of design C double infusion versus the high sensitivity of the corresponding design for the single infusion indicates the significance of the infusion process. The resistivity and strain are directly related to the piezoresistive response and sensitivity. For the design range of measurement (0-100 N), an increase in the graphene concentration will decrease the resistivity across the sensor, requiring an increase in the compressive stiffness to maintain the sensitivity found in the single infusion samples.
The results showed the importance of defining a mechanical compressive saturation limit above the range of measurement to produce sensors with high sensitivity for the compressive sensing range that produces localized strain, supporting the influence of the localized strain found in a previous study [36], rather than distributed strain in directions different to the resistivity that generates dimensional changes by deforming the entire sensor structure. Moreover, for the same compressive stiffness, changing the infusion process affected the sensitivity for the entire range of force.

E. Limitations and Future Work
The manufactured samples presented increased strut diameter in the top and bottom layers compared to the design specifications (Table I). Minor differences in the lattice strut diameter influenced the compressive stiffness. Nevertheless, the samples for the three designs were affected similarly, increasing their dimensions and maintaining the same differences between design variants. Despite the reduced number of samples for each design, the findings from this study indicated the effects of the structural parameters and graphene infusion processes on piezoresistive sensitivity. To improve the statistical significance, future work will include testing a larger sample size to characterize the piezoresistivity of the sensors.

IV. CONCLUSION
The findings from this study indicate that SLS-printed soft metamaterial sensors using TPU lattice structures coated with graphene inks can produce high-sensitivity piezoresistive sensors. Microstructural changes in the lattice strut diameter and top/bottom layer were a determinant factor in the design of the piezoresistive sensitivity and range of measurement of the sensors, resulting in large differences in the resultant compressive stiffness. Across the different sensor designs, the single graphene infusion process achieved the best piezoresistive sensitivity for the lattice design C. More importantly, this study shows the importance of designing structures with sufficient compressive stiffness to match the range of measurement requirements.
The results from this study characterize, to some extent, the piezoresistive response of sensors for a range of measurement from 0 to 100 N. The mechanical compressive saturation directly affected the compressive sensing strain range, while the graphene infusion influenced the sensitivity and linearity of the piezoresistive response of the sensors.
This study demonstrates an approach using AM and graphene infusion to create metamaterial piezoresistive sensors. The sensitivity and response of the sensors show the potential use of wearable sensors for measuring the VGRF at foot pressure points during gait and could be used to design sensors with predictive behavior under specific ranges of measurement. Future work will evaluate the sensors during gait. In addition, the proposed parametric sensor configuration may enable personalized embedded sensing in wearable devices for patient monitoring.