2D material-enhanced multi-fold self-sensing and programmable deployable lattice structure

Abstract

The development of intelligent and programmable smart composite structure that can remember and restore their original shape after being extensively deformed is highly sought after for a wide variety of applications, such as deployable and morphing structures, soft robots, and smart infrastructure. Despite recent advancements, there remains a plethora of unexplored possibilities in the field of deployable structures utilizing shape programmable and intelligent composite materials. The aim of this research is to manufacture a deployable structure that is intelligent enough to monitor the deployment and programmable to be deployed in specific way. Here, a smart deployable auxetic structure is reported that not only possesses thermal and piezoresistive sensing properties but also acts as a thermally activated intelligent shape memory polymer composite (iSMPC). We have fabricated an intelligent fabric and embedded it as reinforcement within a polyurethane-based shape memory polymer matrix to make an intelligent auxetic (A-iSMPC) structure. It has been demonstrated that the intelligent fabric enhances the overall mechanical properties of the auxetic structure and allows monitoring the temperature variation and strain changes during shape programming and recovery. The A-iSMPC offered a negative Poisson’s ratio of − 0.44, shape recovery ratio of 96%, shape fixity ratio of 88% and compaction ratio of 62%. With its shape memory, auxetic, thermal and piezoresistive sensing capabilities, this iSMPC has the potential to be a multifunctional and multipurpose structure for a variety of applications.

Introduction

Deployable structures were introduced to the engineering world in 1824 when Francois Arago developed a collapsible telescope¹. Since then, deployable structures are being employed in various applications ranging from car sunroofs, military tents, convoy shelters and aircraft hangers to space antennas, solar panels and radiators^2–6. However, the deployment of these structures can be challenging, and especially in the case of space structures it is particularly desirable to have a structure that can be remotely monitored during deployment. NASA has documented a number of incidents where antenna, solar array, and boom deployments have failed⁷. Developments in materials science and technology led to the invention of shape memory polymers (SMPs) that, with the aid of external stimuli, can return to their original shape after being significantly deformed to a temporary shape⁸. The addition of conductive fabric enhances the mechanical properties and incorporate sensing ability in the shape memory polymer composites (SMPCs)⁹. Auxetics, having ability to shrink laterally on compressing and vice versa, are also considered beneficial structures in deployable and aerospace applications^10,11. Therefore, this research focuses on exploiting the synergistic effect of auxetics, conductive smart fabric and shape memory polymer to fabricate an intelligent deployable auxetic SMPC structure that can remotely monitor the deployment process.

Thermally activated SMPs have attracted the most recognition, in both research and industry, amongst all SMPs¹². The smart properties of SMPs lie in their unique capability to undergo a phase transition from a stiff, glassy state to a soft, rubbery state, and vice versa. A typical thermally activated SMP passes through four stages during a shape recovery cycle which are briefed ahead. (1) The SMP in its original shape; (2) Heating above transition temperature (T_g) and deforming into desired shape with external force; (3) Lowering the temperature below T_g for shape fixation; (4) Recovering original shape by heating above T_g.

To incorporate some desired properties like thermal and electrical conductivity or to enhance the mechanical properties, SMPs are often reinforced with some nano and hybrid fillers like carbon nanotubes (CNTs)¹³, carbon nanofibers (CNFs)¹⁴, graphene¹⁵, carbon black¹⁶, silicon carbide¹⁷, nickel micro-powder¹⁸ etc. Abdullah et al.¹⁹ produced shape memory polyurethane (SMPU) reinforced with multi-walled carbon nanotubes (MWCNTs) through mixing and injection moulding and reported that the relative shape fixity was improved but the shape recovery rate was reduced significantly. Williams and his group from NASA showed that with addition of graphene nanofiller, the storage modulus and crosslinking density of the shape memory polymer composite (SMPC) was decreased, with improvement in shape recovery and increment in elasticity of nanocomposite²⁰. However, while mixing with SMPs, these nanofillers tend to agglomerate and have a detrimental effect on the mechanical characteristics, reducing the extent of shape recovery and extending the duration of recovery for the SMPC^21,22. To impart better mechanical properties in the SMPs, numerous researchers attempted to reinforce them with fibers and succeeded in significantly improving the strength and modulus along-with better shape fixity and recovery rate^23,24. Lately many research groups have employed glass-fabrics coated with nanomaterials like MXenes, carbon nanotubes (CNTs) and reduced graphene oxide (rGO) to make smart sensing composites^25–27. Recently, our group has developed SMPC laminates by reinforcing SMP with an rGO coated fabric, which not only provided mechanical strength to the SMP but also made the composite capable of sensing the shape recovery simultaneously with the changes in temperature⁹.

With a negative Poisson's ratio and the ability to contract laterally upon compression, auxetic structures offer high energy absorption, variable permeability, and resistance to indentation and fracture, allowing them to be used in a variety of applications including filtration, biomedical, automotive, and aerospace. Rossiter et. al. and Liu et. al. have reported the fabrication of shape memory polymer based auxetic structures by simple techniques like moulding, laser cutting and 3D printing^28,29. Xian Li et al. recently published a review summarizing significant advancements in the design methodologies of soft and stiff auxetic materials including auxetic cellular materials and auxetic composites³⁰.

In this research, we propose an intelligent, programmable, and deployable auxetic composite structure using smart fabric and shape memory polymer. The smart fabric, coated with rGO, serves as a strain and temperature sensing component. This smart fabric is embedded as a reinforcement in SMP matrix to fabricate a laminate of intelligent shape memory polymer composite and an intelligent shape-memory polymer composite auxetic structured unit cell. The embedded sensing capabilities allows to monitor the state of the structure during the shape deployment-recovery process. This research presents a novel approach as, to the best of our knowledge, no previous work has fabricated and tested an auxetic structured shape memory polymer composite with integrated sensing capabilities.

Materials and methods

Materials

MP-4510, a potting type polyurethane-based shape memory polymer comprising of two components i.e., resin and hardener, was acquired from SMP Technologies Inc. Japan. It has a glass transition temperature (Tg) of 45 °C and offers 30 MPa tensile strength. Aqueous paste of very fine quality single layered graphene oxide was procured from Abalonyx Inc. Norway, and it is constituted of 25% GO in 74% water and 1% HCL. The plain weave E-glass fabric having areal weight of 202 g/m² was received from Gurit, UK. The procured GO paste, and glass-fabric were used to fabricate rGO coated smart fabric. The method for fabricating the smart fabric is explained in the supplementary information S.1. It is an improved version of the method previously reported by our group and includes ultrasonication of GO slurry with glass fabric to obtain a much finer GO coated fabric as shown in Fig. 1a ⁹.

Fig. 1.

Schematic showing (a) preparation of rGO coated smart fabric (explained in supplementary information), (b) synthesis of SMP, (c) fabrication of iSMPC laminate, (d) fabrication of A-iSMPC structure, (e) images of iSMPC at macro and micro scale, rectangular sample for DMA testing, dog-bone sample for tensile testing and a programming cycle for shape memory test on DMA. (f) A-iSMPC auxetic going through shape memory cycle and a plot showing varying Poisson’s ratio and piezoresistivity during shape programming and recovery.

Several types of samples are manufactured in this study. For better readability, we have used the following acronyms for each type of samples. SMP refers to shape memory polymer samples fabricated using commercially available resin. iSMPC denotes composite laminates reinforced with in-house developed smart fabric embedded within SMP resin. A-SMP signifies auxetic structures fabricated from commercially available resin. A-iSMPC represents auxetic structures created by incorporating in-house developed smart fabric within SMP resin.

Manufacturing iSMPC laminate

The resin and hardener, with a 1:1 weight ratio, were heated separately at 75 °C for 5 min and degassed in a vacuum chamber at − 0.9 bar for 20 min to eliminate air bubbles, as shown in Fig. 1b. Simultaneously, a 1 × 100 × 90 mm aluminum mould was sprayed with a release agent, and a piece of prepared smart fabric was placed inside. This mould was then placed in the oven at 75 °C for 15 min. Afterward, the degassed components were manually mixed in a cup for 30 s at 120 rpm, resulting in a cloudy white textured mixture, which was immediately poured into the pre-heated mould containing the smart fabric. The mould was then placed in a vacuum chamber at -0.7 bar to remove any entrapped air bubbles from the SMP mixture. Following degassing, the mould was heated in the oven at 75 °C for 40 min, producing a cured intelligent shape-memory polymer composite (iSMPC) laminate shown in Fig. 1c. This laminate was subsequently subjected to various materials characterizations and testing.

Manufacturing auxetic A-iSMPC Structure

A-iSMPC structure was fabricated using a custom-made auxetic shaped mold (shown in Supplementary Fig. S3). Instead of the big rectangular piece of smart fabric used in manufacturing iSMPC laminate, two small strips of smart fabric with dimensions of 8 × 50 mm were used for fabricating A-iSMPC. Copper wires were connected to both ends of the strips, and they were placed in the mold, which had already been sprayed with a release agent. The prepared SMP mixture was poured into the mould to fill it completely. The mould was then kept in the vacuum chamber at a low pressure of − 0.5 bar for 2 min to remove the air bubbles. Higher pressure or prolonged degassing could cause the SMP spilling. After degassing, the mold was heated at 75 °C for 40 min, yielding A-iSMPC as shown in Fig. 1d.

Material characterization and testing

Microstructural characterization

The morphology of the rGO coated smart fabric and the fabric-SMP interface was examined using FEI SEM-Quanta 250 (ESEM). Additionally, Fourier Transform Infrared Spectroscopy (FTIR) analysis was conducted to verify the thermal reduction of GO.

Thermal characterization

Glass transition temperatures for both SMP and iSMPC were determined through thermal analysis using SETARAM Differential Scanning Calorimetry (DSC) 131 Evo. Samples, weighing between 10 and 15 mg, underwent heating from 25 °C to 90 °C at a rate of 3 K/min.

Quasi-static mechanical testing

Mechanical properties such as tensile strength and stiffness for both SMP and iSMPC were obtained by performing tensile testing at room temperature using an Instron universal testing machine (UTM) 5982 with a 5kN load cell and a displacement rate of 2 mm/min. The dog-bone-shaped test samples, conforming to ASTM D638-IV standards (Fig. 1e) were employed. Precise strain measurements were carried out using a Digital Image Correlation (DIC).

Dynamic mechanical analysis

To analyze the viscoelastic characteristics of both SMP and iSMPC, the NETZSCH 242-E Dynamic Mechanical Analyzer (DMA) was utilized. Rectangular samples (20 × 6 × 1.2 mm) were subjected to tension mode testing at a frequency of 1 Hz within a temperature range of 30 °C to 90 °C, using a heating rate of 3 K/min. A sample clamped in the DMA tension mode is illustrated in Fig. 1e.

Thermo-mechanical testing for shape memory behavior

SMP and iSMPC laminate

Rectangular samples (20 × 6 × 1.2 mm) were tested in tension mode using NETZSCH 242-E DMA. The testing program, depicted in Fig. 1e, includes an image of the iSMPC sample installed within the DMA tension mode fixture. The temperature chamber was initially heated to 70 °C and allowed to equilibrate for 15 min. Subsequently, a static force of 3 N was applied and maintained for 15 min at the same temperature. The chamber was then gradually cooled to 30 °C using a cooling rate of 0.2 K/min. After a duration of 290 min, the applied force was removed, yielding a temporarily fixed shape. The sample was held at the same temperature for an additional 20 min to assess its shape fixity, representing the material's ability to retain its temporarily fixed shape. Following this, the chamber was reheated to 70 °C, resulting in the restoration of the original shape.

A-SMP and A-iSMPC auxetic structures

To evaluate the shape memory performance of smart fabric reinforced A-iSMPC, it was necessary to compare it with a benchmark sample and that was an auxetic shape memory polymer (A-SMP) without smart fabric reinforcement. The shape memory behavior of A-SMP and A-iSMPC auxetic structureswas observed using an Instron 5969 UTM connected to a heating chamber, as shown in Fig. 2a. However, for testing shape memory behavior of A-SMP, the DAQ was not employed since A-SMP solely consisted of pure SMP without smart fabric.

Fig. 2.

Images showing (a) the electro-thermo-mechanical testing setup for monitoring resistance changes during compression and shape memory cycles and (b) progressive images of A-iSMPC during complete shape memory cycle. In roman numbering order the images show the A-iSMPC sample (i) after heating above Tg, (ii) getting compressed. (iii) cooling down in fully compressed state, (iv) after force removal, (v) at time ‘t’ during shape recovery and (vi) after complete shape recovery.

The testing procedure involved heating the samples above their glass transition temperature (Tg) and subsequently compressing them at a displacement rate of 15 mm/min. The test was programmed to halt automatically once a pre-set force of 20 N was reached, which was adequate to fold the auxetic structure without causing damage. Following compression above Tg, the samples were allowed to cool down to room temperature, and the compressive force was then removed by restoring the UTM compression plate to its initial position. This temporary shape was maintained for 5 min to measure the rate of fixity. Subsequently, the heating chamber was reheated to 70 °C to facilitate the recovery of the auxetic structures back to their original shape. Images showing different stages of A-iSMPC structure during shape programming and recovery are presented in Fig. 2b. The variation in temperature was captured using the FLIR One thermal imaging camera, with the red dot symbolizing the location featuring the highest temperature in the image, along with its corresponding temperature value as shown in Fig. 6.

Fig. 6.

(a) Thermal images taken with FLIR camera during the complete shape memory cycle. In roman numbering order the images show the A-iSMPC sample (i) after heating above Tg, (ii) getting compressed. (iii) cooling down in fully compressed state, (iv) after force removal, (v) at time ‘t’ during shape recovery and (vi) after complete shape recovery. (b) Comparison between the shape recovery ratio and recovery time for A-SMP and A-iSMPC.

Electro-thermo-mechanical testing

The electro-thermo-mechanical testing setup consisted of an Instron 5969 UTM, an Instron environmental chamber, and a Keysight DAQ 970A data acquisition system, as shown in Fig. 2a. The environmental chamber was utilized to maintain a specified temperature, while the Instron UTM facilitated the compression or folding of auxetic structures. Concurrently, the DAQ monitored variations in the resistance of the smart fabric throughout the shape programming and recovery phases.

This setup was employed for conducting two primary studies, elaborated upon in the subsequent sections.

Auxetic and piezoresistive behavior during shape memory cycle

To demonstrate the capability of A-iSMPC in monitoring shape recovery and strain changes, the smart auxetic structure underwent the shape memory cycles. It was initially heated to 80 °C, then subjected to a 20 N load for compression. Upon compression, it was cooled to room temperature for shape fixation, and subsequently, upon reheating to 80 °C, fully regained its original auxetic shape. Throughout this shape programming and recovery cycle, the changes in the resistance of the A-iSMPC fabric were continuously monitored using the DAQ system. The images of A-iSMPC at different stages during shape memory cycle are shown in Fig. 2b. To validate the auxeticity of A-iSMPC, both axial and lateral strains were measured using marked dots placed at various positions on the structure. A video was recorded during the shape memory cycles to capture the movement of these marked dots. Subsequently, the video was converted into images, which were then analyzed through a self-developed MATLAB code to calculate the axial and lateral strains using the marked dots. This analysis allowed for the calculation of the Poisson's ratio across the entire shape memory cycle.

To analyze strain, five specific locations on the auxetic structure were identified and marked with black markers as shown in Fig. 3. Each image was then subjected to a thresholding algorithm, which designated the marked regions as logical 1 and the rest as logical 0. This process resulted in a logical image where pixels with a value of 1 appeared as white, while those with a value of 0 appeared as black. The thresholded logical image was then processed using the MATLAB function "regionprops," which detected each white dot as an individual object in the image and computed their centroids. These centroids corresponded to the positions of the marked black dots on the auxetic structure, enabling the calculation of axial strain and Poisson’s ratio for the structure.

Fig. 3.

Image analysis for Poisson's ratio calculations.

Each black marker is uniquely labeled with distinct colors applied to the enclosing boxes. Consequently, the centroid of each marker is denoted as ${(x}_i,y_i)$ where i corresponds to the marker number. The dimensions H, L, and t of the structure remain constant throughout the experiment. On the other hand, ${\theta }_1$ and ${\theta }_2$ are the only variables that undergo change during the experiment and are calculated as follows.

${\theta }_1$ was calculated by finding the angle between the vector joining Marker 2 and Marker 1, and the y axis.

$${\theta }_1={\text{cos}}^{-1}(\frac{y_1-y_2}{\sqrt{{\left(x_1,-,x_2\right)}^2+{\left(y_1,-,y_2\right)}^2}})$$ 1

Similarly, ${\theta }_2$ was calculated using the vector joining Marker 2 and Marker 3, and the y axis.

$${\theta }_2={\text{cos}}^{-1}(\frac{y_3-y_2}{w\sqrt{{\left(x_3,-,x_2\right)}^2+{\left(y_3,-,y_2\right)}^2}})$$ 2

Furthermore, $\overline{\theta }$ is calculated by taking the average of ${\theta }_1$ and ${\theta }_2$.

To calculate the axial strain during compression, the distance between marker 4 and marker 5 is observed and calculated using the following formula.

$${ϵ}_Y\left(t\right)=\frac{y_5\left(t\right)-y_4\left(t\right)}{y_5\left(0\right)-y_5(0)}$$ 3

where t stands for time instant at which axial strain is being calculated. Instantaneous Poisson ratio is calculated using the expression developed by Berinski et al. using homogenization procedure of re-entrant honeycomb multi lattices³¹.

$$\nu \left(t\right)=\frac{-1}{\alpha +\text{sin}\left(\overline{\theta },(t)\right)}\frac{2\left(1,-,{\beta }^2\right)\text{sin}\left(\overline{\theta },(t)\right){\text{cos}}^2(\overline{\theta }(t))}{1+{\beta }^2-\left(1,-,{\beta }^2\right)\text{cos}(2\overline{\theta }(t))}$$ 4

where $\alpha =\frac{H}{L}$ and $\beta =\frac{t}{L}$.

Varying temperature and Isothermal strain sensing behaviour

In the end, the A-iSMPC smart structure's capability for temperature change detection and isothermal strain sensing was demonstrated. This was achieved by subjecting the structure to a thermal chamber's heat and applying compressive force using the Instron UTM, while simultaneously monitoring changes in the resistance of the incorporated smart fabric via the DAQ system.

To investigate the impact of cyclic temperature and compression on the piezoresistivity of A-iSMPC, the sample was subjected to a series of experiments. Initially, the sample was subjected to heating within the Instron thermal chamber until a uniform temperature of 85 °C was reached. Subsequently, four cycles of compressive loading and unloading were performed. To achieve this, the Instron UTM was programmed to apply a compressive force at a displacement rate of 15 mm/min. The compression was halted upon reaching a compressive force of 20 N. This specific force value was carefully chosen after experimentation, as it proved sufficient to completely fully fold the auxetic structure. A range of forces was explored, considering both higher and lower values, but 20 N emerged as the optimal choice, preventing structural damage while ensuring complete folding of the auxetic structure. The compressive force was released after a minute, allowing recovery due to the chamber's 85 °C temperature. After a two-minute interval, the compressive force was applied again, repeating the entire cycle four times. Changes in the smart fabric's resistance were continuously monitored throughout the testing process.

Results and discussion

Thermomechanical properties

The stress–strain curves for both pure SMP and iSMPC at room temperature are provided in Fig. 4a. Notably, iSMPC exhibits an approximate three-fold increase in tensile strength compared to pure SMP. The stress–strain behavior of pure SMP shows pronounced ductility, characterized by extensive neck formation prior to fracture. Conversely, the reinforcement of the smart fabric in SMP matrix has notably elevated iSMPC stiffness, leading to a brittle fracture behavior.

Fig. 4.

Compares SMP with iSMPC's mechanical, thermal, and thermo-mechanical properties in terms of (a) stress–strain curves (b) DSC plots, (c) storage moduli, (d) loss moduli and tan delta peaks.

The DSC curves of pure SMP and iSMPC are shown in Fig. 4b. Under a heating rate of 3 K/min, Tg is measured at 47 °C for pure SMP and 44 °C for iSMPC. Figure 4c and d depict the DMA results, illustrating the influence of temperature on storage moduli Eʹ, loss moduli E″, and tan δ for SMP and iSMPC, respectively. The Tg can be measured from the DMA results using multiple approaches, such as the onset method or inflection method based on the storage modulus curve, or by identifying the peak in the loss modulus curve or tan δ curve as Tg. It is commonly established that Tg (Eʹ) < Tg (E″) < Tg (tan δ). The Tg values obtained from the loss modulus peak closely align with those from DSC outcomes and are in proximity to the Tg indicated by the SMP manufacturer's data sheet. The incorporation of rGO-coated fabric in SMP induces a slight decrease in Tg. This is attributed to the higher thermal conductivity of the smart fabric, which enhances the thermal sensitivity of iSMPC, consequently leading to a marginal reduction in Tg³².

Figure 4c highlights a notable increase in storage modulus at room temperature upon the reinforcement of smart fabric within the SMP matrix. Typically, a material's storage modulus escalates alongside its stiffness while diminishing as temperature or molecular mobility rises. The introduction of rGO-coated fabric in the SMP matrix curtails polymeric chain mobility, thereby enhancing the stiffness of iSMPC. Furthermore, as temperature increases, the storage moduli of both SMP and iSMPC experience reduction. However, within the range of the glass transition temperature, this decrease is more pronounced and substantial for iSMPC. Around 64 °C, Eʹ of SMP reduces to values of two-orders, eventually reaching 9 MPa at 90 °C. In contrast, the Eʹ for iSMPC decreases to the lowest value of 320 MPa at 90 °C.

Figure 4d reveals that the loss modulus and tan δ curves exhibit a rise with escalating temperature until reaching the glass transition temperature (Tg). Subsequently, they decline as the material becomes more deformable and its viscous behavior diminishes. E″ is a measure of the amount of energy that is dissipated during deformation of the material, often stemming from the internal friction associated with polymer chain movement. The tan δ, a ratio of loss modulus to storage modulus, essentially quantifies the energy stored and subsequently recovered in contrast to the energy dissipated. For iSMPC, the tan δ peak broadens while its height decreases compared to SMP. This can be attributed to the lower damping effect (energy loss in the form of heat) in iSMPC than in SMP at Tg. The mechanical and thermomechanical properties of SMP and iSMPC are given in Table 1.

Table 1.

Mechanical and thermomechanical properties of SMP and iSMPC.

Property	SMP	iSMPC
Tensile strength (MPa)	28 ± 3	75 ± 5
Young’s modulus (MPa)	680 ± 90	3350 ± 200
Storage modulus (MPa)	2135 ± 150	5250 ± 500
Tg from DMA E″ (°C)	47.8 ± 0.7	44.5 ± 1.7
Tg from DSC (°C)	45.3 ± 0.9	43.9 ± 0.2

Shape memory behavior

SMP and iSMPC laminates

To investigate the shape memory behavior of SMP and iSMPC sheets, rectangular strips were subjected to DMA testing in tensile mode. The resulting shape memory cycles for SMP and iSMPC are shown in Fig. 5a and c, respectively. Correspondingly, the strain cycles during cooling and heating stages are illustrated in Fig. 5b and d, respectively.

Fig. 5.

(a,c) Shape memory cycles and (b,d) strain vs temperature cycle for SMP and iSMPC.

Maintaining the temperature above Tg increases the mobility of the polymeric chains, while the applied 3 N load induces strain in the samples by causing deformation. Subsequent temperature reduction from 70 °C to 30 °C locks the polymeric chains in the strained configuration, leading to what is known as the temporary fixed shape. Upon removing the applied load and reheating to 70 °C, the polymer chain mobility reactivates, facilitating the recovery of the initial shape. Evidently, the incorporation of smart fabric significantly curtails overall deformability, resulting in a notable reduction in maximum strain % for iSMPC (0.45%) compared to SMP (7.5%). As a result of this, in Fig. 5c, a sharp dip is observed for iSMPC upon removal of the applied load.

Two most important aspects of shape memory behavior characteristics are shape recovery ratio (R_r) and shape fixity ratio (R_f). The shape recovery ratio signifies the degree to which a material can restore its initial shape after experiencing considerable deformation, while the shape fixity ratio gauges the material's capacity to retain its transiently deformed shape. These key characteristics are quantified using the equations presented below:

$$R_r=\frac{{\mathrm{\epsilon }}_c-{\mathrm{\epsilon }}_d}{{\mathrm{\epsilon }}_c}\times 100(\%)$$ 5

$$R_f=\frac{{\mathrm{\epsilon }}_c}{{\mathrm{\epsilon }}_b}\times 100(\%)$$ 6

As indicated in the Fig. 5a,c, ${\mathrm{\epsilon }}_a$ represents the strain in the original shape of the sample, which is consistently zero unless retesting an incompletely recovered sample. ${\mathrm{\epsilon }}_b$ signifies the maximum strain induced in the sample while applying force during shape fixation. ${\mathrm{\epsilon }}_c$ corresponds to the strain in the temporarily fixed shape, marginally lower than the maximum strain ${\mathrm{\epsilon }}_b$, unless the material exhibits ideal 100% shape fixity. ${\mathrm{\epsilon }}_d$ stands for the final strain at the conclusion of the shape memory cycle, attained after reheating the sample above its Tg to restore its original shape. Using the aforementioned equations, the shape recovery and shape fixity ratios for SMP were calculated as 87.13% and 96.27%, respectively, while for iSMPC, they were found to be 90.24% and 88.50%. The greater strain produced by the same applied force in pure SMP, as compared to iSMPC, leads to higher viscous dissipation and consequently diminished shape recovery. Hence, the shape recovery ratio is lower for SMP in contrast to iSMPC. Furthermore, the incorporation of rGO fabric strengthened the SMP polymer matrix and imparted increased rigidity. This enhanced stiffness pushes the temporarily fixed shape closer to its original form, even without heating the sample, contributing to the reduced shape fixity ratio of iSMPC. Figure 5b,d illustrates the strain variation as a function of temperature for both SMP and iSMPC. The upper segment of the curves corresponds to the shape fixing phase, occurring during temperature reduction from 70 °C to 30 °C. The lower segment of the curves depicts the shape recovery phase, taking place as the temperature is raised from 30 °C to 70 °C. Notably, the red dotted circle denotes the abrupt decline in strain resulting from the cessation of applied force.

A-SMP and A-iSMPC auxetic structures

A complete shape memory cycle of A-iSMPC sample is shown in Fig. 6. The measurement of shape recovery ratio and shape fixity ratio was accomplished by assessing the differences in height within the auxetic structures throughout the shape memory cycle. The formulae for determining both these parameters are given below:

$$R_r=\frac{{\text{h}}_t-{\text{h}}_c}{{\text{h}}_o-{\text{h}}_c}\times 100(\%)$$ 7

$$R_f=\left(\frac{{\text{h}}_o-{\text{h}}_{\mathit{afr}}}{{\text{h}}_o}\right)/\left(\frac{{\text{h}}_o-{\text{h}}_c}{{\text{h}}_o}\right)\times 100(\%)$$ 8

Here ${\text{h}}_o$, ${\text{h}}_c$, ${\text{h}}_{\mathit{afr}}$ and ${\text{h}}_t$ represent the height of the auxetic structure in original shape, in compressed state, after the compressive force removal and at any time t while recovering back to original shape. The numerator in R_f formula represents the maximum strain imposed on the material while the denominator signifies the strain in the fixed temporary shape. Applying the above stated equations, the shape recovery ratios were computed as 96.99% for SMP and 95.62% for iSMPC, while their corresponding shape fixity ratios were determined as 94.26% for SMP and 87.91% for iSMPC. A comparison of the shape recovery ratio vs recovery time for A-SMP and A-iSMPC is illustrated in Fig. 6b. The incorporation of the reinforced smart fabric significantly reduced the shape recovery time, with only a slight decrease in the overall shape recovery ratio. The comparison between shape recovery of A-SMP and A-SMPC can be viewed in the provided supplementary video, SV-1.

Auxetic behavior during shape memory cycle

The Poisson’s ratios for A-SMP and A-iSMPC during whole shape memory cycles are plotted as a function of the applied compressive force in Fig. 7. Following the attainment of the designated isothermal temperature (approximately after 25 min), the force is applied, inducing strain in both the x and y directions. This leads to a shift in Poisson’s ratio from − 0.44 and − 0.35 to − 0.002 and − 0.007 for A-iSMPC and A-SMP respectively. Once a pre-set force of 20 N is reached, it is maintained for 40 min, during which the temperature gradually drops from 80 °C to 30 °C. Over this interval, the Poisson’s ratios remain relatively unchanged, reflecting minimal lateral and axial strain variations due to the auxetic structure's complete compression. The nearly negligible Poisson’s ratio at this point indicates that the auxetic structure has become effectively incompressible, rendering it resistant to further axial and lateral deformations under additional compressive force. Upon force removal at 65 min, an abrupt reduction in Poisson’s ratio occurs, attributed to the rise in axial strain during elastic recovery. Subsequently, as the temperature increases, the auxetic structures regain their initial forms, causing the Poisson’s ratios to revert to their original values. Notably, the shape recovery process of A-iSMPC exhibits a slightly steeper Poisson’s ratio curve compared to A-SMP, indicative of the faster shape recovery of A-iSMPC. The Poisson’s ratio calculations are confined to the timeframe between 25 and 77 min, as no significant strain changes occur before or after this period. A video of the variation in Poisson's ratio during the complete shape memory cycle of A-iSMPC is provided in the supplementary information as SV-2.

Fig. 7.

Poisson's ratio of A-iSMPC during complete shape memory cycle (the roman numbers correspond to the respective shape memory cycle steps shown in Figs. 2 and 6).

Piezoresistive behavior during shape memory cycle

The variation in resistance exhibited by the smart fabric in response to applied compression during successive shape memory cycles is shown in Fig. 8. These cycles are described by the ascending and descending segments of the heating curve, signifying the programming and recovery phases, respectively.

Fig. 8.

Piezoresistive behavior of A-SMP during (a) single shape memory cycle and (b) multiple shape memory cycles (the roman numbers correspond to the respective shape memory cycle steps shown in Figs. 2 and 6).

As the temperature increased, the resistance of the smart fabric began to decrease (i). Upon applying a compressive force of 20 N to compress the auxetic structure, a sharp increase in resistance was observed as the top compression plate was engaged with the sample (ii). The resistance then experienced a slight dip within the compressive force range of 4–7 N before continuing to rise until complete compression was achieved. This force was maintained to fix the shape while the temperature was reduced to room temperature. During shape fixing, with the exception of the first cycle, the resistance of the smart fabric largely returned to its initial level prior to force application. Due to the absence of a chilling unit in the thermal chamber, the cooling process was expedited by briefly opening the furnace door during shape fixing, although it still took nearly 40 min to cool down to 30 °C. Throughout this cooling phase, the relative resistance gradually increased (iii).

Subsequent to shape fixing, the furnace door was closed and the applied force was removed before initiating the heating cycle for shape recovery. This caused a slight temperature increase, as indicated at the beginning of the second, third, and fourth heating cycles. As the glass transition temperature was reached, the auxetic structure began to unfold, leading to a drop in relative resistance. However, a temporary increase in resistance occurred when the auxetic structure reached a partially recovered position (v). Once the structure regained its original shape, the resistance began to decrease again with further temperature increases. The repeatability of this piezoresistive behavior is demonstrated across multiple shape memory cycles in Fig. 8b. The smart fabric exhibits its highest conductivity in its original shape.

However, during the programming cycle, individual fibers experience stretching due to force application, resulting in reduced interconnectivity and conductivity. Even during recovery, the rGO-coated fibers may temporarily lose interconnectivity, leading to a sudden spike in relative resistance, which subsequently diminishes with increasing temperature. The variation in relative resistance during one complete shape memory cycle of A-iSMPC is provided in the supplementary video SV-3.

Effect of temperature and compressive loading on piezoresistivity of A-iSMPC

The effect of varying temperature, and the application and removal of compressive loads can be observed in Fig. 9a. As the temperature surpasses 60 °C, the resistance diminishes. Conversely, as the temperature descends from 100 °C to 85 °C, the resistance tends to increase, indicating an inverse relationship between applied temperature and resulting resistance. In the compression cycle shown in Fig. 9b it is noticeable that resistance rises with compression. However, a distinct decline is evident within the force range of 3–7 N, attributable to the formation of networks as the rGO-coated fiber strands come closer during compression. A similar behavior is observed for all four compressive loading and unloading cycles as shown in Fig. 9a. During compression, the A-iSMPC undergoes folding, leading to the stretching of the smart fabric at the bending points within the auxetic structure. This stretching of the fabric creates gaps between the conductive fiber strands, resulting in an increase in resistance.

Fig. 9.

Effect of temperature and compression on A-iSMPC for (a) multiple cycles and (b) single cycle (magnified) (the roman numbers correspond to the respective shape memory cycle steps shown in Figs. 2 and 6).

The axial and lateral strains resulted by the applied compressive stress are plotted in Fig. 10a,b. Initially, for stress values below 5 kPa, both lateral and axial strains increase at almost the same pace. However, as stress continues to increase, the lateral strain experiences a rapid increase. Notably, the overall strain change is more pronounced along the axial direction due to greater deformation capacity in the y-axis compared to the x-axis. Figure 10c shows the evolution of Poisson’s ratio and relative resistance change during a complete loading and unloading cycle carried out at a uniform temperature of 85 °C. The Poisson’s ratio increases from − 0.44 to almost zero, which signifies that this structure is no more compressible. In contrast, during unloading or recovery, a peak is observed, attributable to the rapid disintegration and reconnection of conductive fabric networks.

Fig. 10.

Compression testing and piezoresistive response of A-iSMPC at 80 °C. (a) Axial Stress–Strain curve, (b) Lateral Stress–Strain curve, (c) effect of stress on relative resistance and Poisson’s Ratio. Relative resistance as a function of applied (d) axial (e) lateral strain and (f) stress (the roman numbers correspond to the respective shape memory cycle steps shown in Figs. 2 and 6).

Furthermore, the changes in relative resistance of A-iSMPC corresponding to applied axial strain, lateral strain and stress are illustrated in Fig. 10d–f respectively.

Overall, the relative resistance increases with the increase in stress or strains, but a similar trend is observed in all of these plots. Notably, within the range of compressive stress values spanning 5–15 kPa, corresponding to axial strain values of 20–55% and lateral strain values of 20–38%, a dip in relative resistance occurs. This dip arises due to the formation of conductive networks as the rGO fiber strands come into closer proximity during compression. Subsequently, with further compression, the conductive fibers within the region of the two bends in the auxetic structure develop gaps, resulting in elevated relative resistance. The sensitivity of piezoresistive response was quantified by measuring the gauge factor for both temperature and strain. The gauge factor is 0.5 in case of temperature sensitivity, while it ranges between 0.3 and 2.5 for strain sensitivity. The gauge factor values vary as the relative resistance changes because of bending of smart fabric within the auxetic sample throughout the shape memory or compression cycle.

The gauge factor values are not quite high because in A-iSMPC the piezoresistive behavior comes from the contact based conductive network of rGO flakes coated onto glass fabric. As the rGO flakes are well in contact with each other, the disruption of flow of electrons requires high deformation. However, if the piezoresistive behavior comes from tunnelling effect (in case of low concentration of conductive filler), then the gauge factor values can be significantly higher³³.

Conclusions

This study introduces a novel approach that combines shape memory polymers, self-sensing piezoresistive smart fabric, and auxetic structures to create a multifunctional, intelligent, and deployable auxetic composite. Deployable structures are crucial for ensuring reliable deployment in challenging environments, including remote or space applications. Therefore, deployable structures that can monitor the whole process of deploying and stowing are highly desirable. The research involved incorporating rGO-coated smart fabric into a TPU-based shape memory polymer to fabricate A-iSMPC. The addition of the smart fabric not only increased strength and stiffness but also accelerated shape recovery. Temperature and strain sensing capabilities were evaluated by subjecting the A-iSMPC to controlled heating and compression in a thermal chamber connected to an Instron UTM, while monitoring changes in fabric resistance using a DAQ system. The A-iSMPC demonstrated the ability to monitor shape programming and recovery through its piezoresistive response. Above the glass transition temperature (Tg), applying a compressive stress of approximately 30 kPa led to 60% axial strain and 40% lateral strain in the A-iSMPC. The relative resistance initially decreased with increasing compressive stress until full folding occurred, at which point it suddenly increased. Notably, the fabricated A-iSMPC exhibited a negative Poisson’s ratio of -0.44, a shape recovery rate of 96%, a shape fixity rate of 88%, and a compaction ratio of 62%. This work was restricted to the fabrication of a single unit cell of A-iSMPC, however by making multicell lattices of A-iSMPC we can create multifunctional structures that can be used as deployable solar arrays, antennas booms and other engineering applications.

Author contributions

A.H: conceptualization, methodology, data curation, software, validation, formal analysis, investigation, writing—original draft. S.K: methodology, data curation, software, validation, formal analysis, investigation, writing—original draft. K.K: conceptualization, methodology, writing—review and editing, visualization, resources, investigation, supervision, project administration, funding acquisition.

Data availability

The datasets used and/or analyzed during the current study available from the corresponding author on reasonable request.

Competing interests

The authors declare no competing interests.

Supplementary Information

The online version contains supplementary material available at 10.1038/s41598-024-70607-z.