Viscoelastic and thermo-mechanical piezoresistive behavior of reduced graphene oxide-coated glass fiber reinforced polymer-based sandwich structures under flexural loading

Abstract

This study investigates the time-dependent and thermo-mechanical piezoresistive behavior of glass fiber-reinforced polymer (GFRP) coated with partially reduced graphene oxide (rGO) -based honeycomb sandwich composite structures subjected to flexural loading. Sandwich composites with unidirectional rGO-coated GFRP facesheets were tested under monotonic loading at various temperatures, as well as in stress relaxation and cyclic bending conditions. The electromechanical response was strongly influenced by fiber orientation and loading conditions. The isothermal tests on 0° Nomex^® core samples confirmed a negative temperature coefficient, with the thermal coefficient of resistance decreasing from −0.00862°C^-1 at 35°C to −0.00687°C^-1 at 45°C, and showed that elevated temperatures delayed the fractional change in resistance (FCR) and reduced the peak stress by ∼10.6% from 25°C to 35°C and by ∼27.6% from 25°C to 45°C, while preserving the sensing functionality. Stress relaxation tests conducted using both Nomex^® and aluminum cores, revealed orientation-dependent FCR trends i.e. the 0° configurations exhibited an early increase of ∼0.4% for the Al core and ∼1.15% for the Nomex^® core within the first 30 min before plateauing, while 90° configurations showed a continuous reduction in FCR, ∼−0.1% over the relaxation period, due to matrix relaxation. Cyclic loading of the Nomex^® core samples highlighted reversible resistance changes, with baseline drift of ∼10% in the 0° configuration compared to ∼0.18% in the 90° configurations confirming greater visco-piezoresistive effects in the latter. A visco-piezoresistive model, based on Burgers’ viscoelastic model, accurately captured the time-dependent FCR and stress variations under both relaxation and cyclic conditions. The findings of this study advance the understanding of the long-term piezoresistive response of multifunctional sandwich composite structures, supporting their application in structural health monitoring systems.

Graphical Abstract

Keywords

sandwich structures structural health monitoring graphene visco-piezoresistive modeling thermomechanical behavior time-dependent behavior

Highlights

• Monotonic flexural tests showed temperature-dependent sensing, delayed FCR onset, and lower loads at high temperatures.

• Stress relaxation tests showed orientation-dependent FCR: increasing at 0°, decreasing at 90° due to matrix-driven compaction.

• Core type affected 0° relaxation: Nomex showed more stress and FCR drop than aluminum due to its viscoelasticity.

• Cyclic flexural tests showed stable, reversible FCR with more drift and relaxation at 90°.

• A Burgers-based visco-piezoresistive model captured time-dependent electromechanical response.

Introduction

Sandwich structures are widely used in aerospace, marine, and automotive fields due to their high stiffness-to-weight ratio and energy absorption.^1–3 However, their layered architecture makes them vulnerable to internal damage, such as core shear, delamination, and impact-induced damage, that often remains undetectable by visual inspection.^4–6 These challenges highlight the need for integrated monitoring systems to assess internal degradation and ensure structural integrity. Conventional structural health monitoring (SHM) systems, such as strain gauges and fiber optic, are effective but add weight, complicate manufacturing, and may introduce stress concentrations.^7–12 These drawbacks are particularly restrictive for lightweight applications, motivating efforts to embed sensing capabilities directly into the material system for distributed, real-time monitoring.¹³

Recent work has developed multifunctional sandwich structures with self-sensing cores, facesheets or both. While smart cores utilize materials with tailored thermal or electromagnetic properties, self-sensing facesheets often incorporate nanomaterials, such as graphene and its derivatives and carbon nanotubes that enable intrinsic piezoresistive behavior, alongside load-bearing functionality.¹⁴ Carbon-based nanomaterial-coated fabrics embedded in laminates exhibit strain-sensitive resistance changes under monotonic loading, driven by conductive network rearrangement and damage progression.^15–20 When used as sandwich facesheets, they also respond to flexural and compressive loads, with sensitivity influenced by geometry and fiber orientation.^21–23 Ud Din^21,22 showed that the piezoresistive response is influenced by the span length, beam width and core thickness. Complementary studies have also examined the modal and nonlinear dynamic responses of skew sandwich structures through combined theoretical and experimental approaches.^24,25

Under long-term loading, these composites exhibit time-dependent responses, such as stress relaxation and resistance drift, driven by viscoelasticity and network recovery.^26–28 Can-Ortiz²⁶ reported that in CNT-modified laminates, the resistance mirrored the stress decay, reflecting interfacial effects and network dynamics. Cyclic loading induces resistance fluctuations that track mechanical loads, with stability influenced by filler content and fiber-matrix interactions. Rodríguez-González et al.¹⁹ observed reversible response in MWCNT-modified laminates beyond 50 cycles, while MXene- and rGO-based sensors showed consistent signals with gradual drift due to the repeated network disruption.^28,29

Temperature variations also influence the coupled material responses. Analogous multiphysics studies on hybrid nanofluid systems have also reported temperature-dependent nanoparticle transport properties.³⁰ In semiconductors and functionally graded piezoelectric, thermoelastic frameworks capture the stress-heat-electrical interactions,^31,32 and related thermo-mechanical analyses have also been performed on hybrid smart sandwich structures.³³ For composites with carbon-based nanomaterials, electromechanical coupling is governed by temperature-dependent charge transport, with rGO in particular exhibiting a negative temperature coefficient (NTC).^34,35

Despite the growing interest in self-sensing sandwich structures, most studies have focused on monotonic loading, while the combined effects of time-dependence and the thermomechanical conditions remain largely unexplored. This study investigates the thermo-mechanical and time-dependent piezoresistive behavior of rGO-coated glass fiber facesheets in sandwich structures through stress relaxation, cyclic and thermomechanical flexural loading. The resistance evolution during stress relaxation and cyclic tests are further modeled to capture the visco-piezoresistive behavior. By addressing thermal effects, viscoelastic time-dependence, and cyclic electromechanical behavior, the work provides new understanding of the mechanisms governing self-sensing performance of multifunctional sandwich structures.

Materials and methods

Materials

The study makes use of graphene oxide (GO), unidirectional (UD) E-glass fibers, an epoxy resin system, and two different honeycomb cores. Graphene oxide paste was procured from Abalonyx, Norway. The fiber reinforcement used in this study consists of a UD E-glass fiber with an areal weight of 629 g/m² (Arvind PD Composites Pvt. Ltd, India) combined with GURIT PRIME™ 37 epoxy and AMPREG™ 3X slow hardener, mixed in a 100:29 weight ratio (Gurit^®, UK). The sandwich structures were based on either a Nomex^® honeycomb core (4.8 mm cell size, 48 kg/m³ density, 10 mm thickness) or an aluminum honeycomb core made from 5052-grade alloy (3.2 mm cell size, 72.1 kg/m³ density, 10 mm thickness) (Easy Composites Ltd, UK).

Laminate manufacturing

To coat the glass fiber with rGO, a GO solution was prepared by dispersing 1 g of graphene oxide paste into 50 ml of DI-water. Then, sonication was carried out at 47°C for 120 min to promote uniform dispersion of the mixture. The UD E-glass fabrics were immersed in the GO solution for 24 h, ensuring complete saturation and a uniform coating. Subsequently, the coated fabrics were thermally-reduced at 170°C for 24 h to convert the GO into rGO, thereby enhancing its electrical conductivity. Figure 1(a) illustrates the dip coating process of rGO-coated glass fabric. After reduction, the rGO-coated fabrics exhibited initial resistance readings in the range of 1–2 MΩ.

Figure 1.

Manufacturing sandwich composites structure, (a) partially reduce graphene oxide coated glass fabric, (b) manufacturing of the composite facesheet using the vacuum assisted resin transfer molding process (VARTM) and (c) fabrication process using cold pressing at room temperature for 24 h, with two honeycomb core materials: (i) aluminum and (ii) Nomex^®.

In order to ensure electrical connectivity, copper wires (0.8 mm diameter) and adhesive copper tapes (1 mm thick) were attached to the rGO-coated fabrics, spaced 100 mm apart. The rGO-coated fabrics were then integrated into a five-layer laminate, where the rGO-coated layer was placed at the mid-plane of the laminate. The laminates were fabricated using vacuum-assisted resin transfer molding (VARTM), Figure 1(b), to infuse the epoxy. The final laminate, with fiber orientations of either 0° or 90°, depending on the testing configuration, exhibited an average thickness of 2.25 mm. Further details regarding procedures for sensor fabrication and composite manufacturing are given in previous studies by the research group.^16,21–23

Sandwich structure fabrication

The sandwich structures were fabricated by employing the self-sensing laminate as the lower facesheet and a standard uncoated laminate as the upper facesheet in the sandwich structure, Figure 1(c), following the procedure in our previous work.²³ This configuration was adopted based on studies showing that the top facesheet exhibited a minimal piezoresistive sensitivity during loading, since it undergoes a lower strain compared to the distal facesheet.²¹ The self-sensing laminate was employed as the lower facesheet to maximize its effectiveness in load and damage sensing.

The bonding process was carried out by directly applying a thin layer of epoxy resin (PRIME™ 37) mixed with AMPREG™ 3X slow hardener to the contact surfaces of the laminates and core materials. Two core types, aluminum honeycomb and Nomex^® honeycomb were used, as described in Section 2.1. The sandwich composite structure was cold pressed under a pressure of 0.2 MPa and maintained for 24 h,²³ as shown in the cure cycle shown in Figure 1(c). Once the structure was bonded, samples with dimensions of 200 × 75 mm were precisely cut from the composite panels using a diamond slitting wheel to ensure smooth edges and dimensional accuracy. Figure 1(c) (i) and (ii) shows the manufactured sandwich structures with aluminum and Nomex^® honeycomb cores, respectively.

Experimental setup

Mechanical and piezoresistive properties of the self-sensing sandwich composite structures were assessed through three-point bending tests, as shown in Figure 2(a)–(c), using an Instron 5969 universal testing machine with a 50 kN load cell, following ASTM C393 testing standards. The support span was maintained at 180 mm, with the rGO-coated facesheet employed as the lower facesheet, Figure 2(b). Resistance monitoring during the tests was carried out using a Keysight DAQ970 A data acquisition system.

Figure 2.

Experimental setup and program adopted in the study. (a) Schematic of facesheet configuration at two fiber orientations: 0° and 90°. (b) Three-point bending test setup showing facesheet orientation relative to loading direction, and (c) schematic representations of the three loading history profiles: (i) thermomechanical loading, (ii) stress relaxation, and (iii) cyclic loading.

Experimental program

Thermo-electromechanical response under monotonic bending

Monotonic three-point bending tests have been previously conducted at room temperature, 25°C, to examine the electromechanical behavior of sandwich composite structures with reduced graphene oxide GFRP face sheets with fiber orientations of 0° and 90°.²³ In the present study, the investigation is extended to examine the influence of temperature on the piezoresistive behavior in the 0° configuration. To decouple the thermal and mechanical contributions to FCR, a two-phase testing approach was employed. First, the samples were heated to target temperatures of 35°C and 45°C and held isothermally for 18 min to ensure thermal equilibrium. During this thermal stabilization phase, the FCR was monitored in the absence of external mechanical loading, permitting the characterization of temperature-induced resistance changes. Following this stage, monotonic three-point bending was carried out at a constant loading rate of 2 mm/min, as illustrated in Figure 2(c) (i).

Stress relaxation tests

Room temperature stress relaxation tests were carried out to study the visco-piezoresistive behavior of the rGO-coated facesheets at two fiber orientations: 0° and 90°, Figure 2(a). Figure 2(c) (ii) shows a schematic of the loading history profile of the stress relaxation test conducted on both fiber orientations. Tests were performed on sandwich structures with 0° fiber orientation facesheets using both Nomex^® and aluminum honeycomb cores to evaluate whether the viscoelasticity of the phenolic resin in the Nomex^® core influenced the measured piezoresistivity. Additionally, facesheets with 90° fiber orientation were tested with Nomex^® honeycomb cores. All relaxation tests were conducted at room temperature for 100 min. The structures were loaded to 50% of the peak loads observed during monotonic tests, based on our previous study.²³ This level was selected to ensure that stress relaxation occurred within the elastic region, thereby minimizing irreversible damage and isolating viscoelastic and piezoresistive effects. The displacement was then held constant for 2 h to monitor the stress relaxation behavior and FCR over time.

Cyclic tests

Cyclic flexural tests were undertaken to investigate the durability and sensing performance of the self-sensing sandwich composite structures subjected to repeated loading/unloading, Figure 2(c) (iii). These tests were conducted at room temperature on samples with 0° and 90° facesheets, Figure 2(a), both with a Nomex^® honeycomb core. The structures were subjected to 1000 loading-unloading cycles corresponding to 50% and 25% of the failure load determined during the monotonic tests,²³ respectively. These levels were chosen to maintain cyclic loading within the elastic regime, enabling long-term electromechanical stability to be assessed without inducing progressive structural damage.

Modeling of visco-piezoresistivity under relaxation and cyclic loading

The time-dependent evolution of electrical resistance in rGO-coated composite structures is governed not only by the applied load but also by the intrinsic viscoelasticity of the matrix and coating network. In this context, we introduce the term “visco-piezoresistivity” to describe the resistance relaxation phenomenon that arises due to viscoelastic deformation. Specifically, visco-piezoresistivity refers to the continued change in the electrical resistance under constant strain or stress, as a result of time-dependent redistribution of the internal stresses and conductive paths within the network.

To model this behavior, we adopt a model analogous to the Burgers’ viscoelastic formulation, applied here solely to the FCR, as a function of time. The formulation captures three main contributions: an instantaneous elastic change, an exponential viscoelastic component, and a linear drift term, and is expressed as^26,28:

\frac{Δ R (t)}{R_{0}} = a + b e^{- α t} + ct,

(1)

where,

a

represents the instantaneous elastic contribution to resistance change,

b

is the magnitude of the transient viscoelastic effect,

α

is the relaxation rate (with relaxation time

τ_{R} = 1 / α

), and

c

accounts for the permanent component of resistance evolution over time. All of the parameters

a, b, α,

and

c

were treated as independent fitting constants and were determined from experimental data without applying constraints on their initial values.

This model was implemented using experimental data obtained from both the stress-relaxation phase and the mean FCR in the cyclic three-point bending tests described in Section 2.4.2. In the cyclic case, only the mean evolution of the FCR across cycles was considered, capturing the long-term electromechanical drift, whereas short-term cyclic fluctuations were not explicitly modeled.

To better interpret the coupling between mechanical relaxation and piezoresistivity, a similar formulation was adopted for the normalized stress decay at a constant displacement. The stress relaxation behavior was modeled using²⁸:

\frac{Δ σ (t)}{σ_{0}} = a + b e^{- α t} + ct,

(2)

here,

σ (t)

is the measured stress at time

t

σ_{0}

is the initial stress, and the fitting constants

a, b, α,

and

c

carry the same physical interpretation as in the visco-piezoresistive model.

The stress in the distal facesheet was calculated using classical sandwich beam theory, following established formulations reported in the literature^36,37 and our earlier work.²³

Results and discussions

Thermo-electromechanical response under monotonic bending

Thermal piezoresistive behavior

Before conducting the thermomechanical flexural tests, the sandwich structures were heated to the required temperature (i.e. 35°C or 45°C) and maintained for 18 min to achieve an isothermal state. Electrical resistance was monitored throughout this process to compute the thermal coefficient of resistance (TCR). The temperature and FCR profiles are shown in Figure 3(a). A negative TCR (NTC) was observed in this case, which indicates that the resistance decreases with increasing temperature, typical of partially-reduced rGO. At 35°C, the TCR was −0.00862 $° C^{- 1}$ , reflecting the dominance of thermally-activated hopping conduction, where charge carriers gain energy to overcome localized energy barriers. As the temperature increased to 45°C, the TCR values reduced to −0.00687 $° C^{- 1}$ , suggesting a potential shift or saturation in the conduction mechanism. This behavior arises from the semiconducting nature of rGO, where residual oxygen functional groups and a finite bandgap introduce localized electronic states that govern charge transport.^38–40 Figure 3(b) illustrates this mechanism: at lower temperatures, charge carriers are hindered by oxygen/hydroxyl-related energy barriers between rGO flakes, limiting conduction. Upon heating, these carriers gain sufficient energy to hop across barriers, enabling enhanced charge transport and reduced resistance. This thermally-activated process is central to the NTC behavior observed during the heating phase.

Figure 3.

(a) Temperature and corresponding FCR profiles during the heating phase for rGO-coated GFRP sandwich structures at 25°C, 35°C, and 45°C, (b) Schematic illustration of the piezoresistive mechanism during heating and thermomechanical piezoresistive behavior of self-sensing GFRP facesheets/Nomex^® sandwich composite structures under monotonic flexural loading condition with 0° fiber orientation at (c) 25°C,²³ (d) 35°C, (e) 45°C, and (f) maximum tensile stress at the mid-span length of the bottom facesheet.

Thermomechanical piezoresistive behavior under monotonic bending

Figure 3(c)–(e) shows the electromechanical response of the sandwich composite structures with 0° self-sensing distal facesheets under monotonic flexural tests at 25°C, 35°C, and 45°C, respectively. The 25°C case, which has been reported in our earlier work,²³ is included here as a reference to enable direct comparison with higher temperature tests. Since the sensing layer is embedded on the tensile side, the measured FCR captures the localized network disruption under tensile flexural strain. A clear temperature-dependent trend is observed. With increasing temperature, the peak load response decreases, from ∼0.88 kN at 25°C to ∼0.64 kN at 45°C, while the displacement at failure increases, indicating matrix softening.

At all temperatures, the FCR increases steadily during loading, peaking near failure due to progressive stretching of the rGO-coated fibers, separation of adjacent flakes, and tunneling disruption.⁴¹ However, the onset of the FCR curve was progressively delayed at higher temperatures, suggesting reduced strain transfer as the matrix softens. Following failure, both the load and FCR decrease sharply. Unlike tensile fracture, where network rupture leads to a sharp resistance increase,^7,18,42–44 the observed FCR decrease is due to rapid strain release and partial reconnection of conductive pathways.²³ As shown in Figure 3(f), the maximum stress, decreases with temperature, confirming thermally-driven softening effecting both the mechanical and sensing behavior.

To further investigate failure, Figure 4(a)–(c) presents post-failure images at each temperature. At 25°C, Figure 4(a), failure was dominated by localized core shear beneath the loading point, with limited cell wall distortion and no visible debonding, reflecting a relatively stiff matrix and intact facesheet-to-core bond. At 35°C, Figure 4(b), core shear was again evident, accompanied by facesheet-to-core debonding near the tensile region, suggesting a reduced adhesive strength. At 45°C, Figure 4(c), failure became more distributed, with extensive core crushing, pronounced debonding, and visible wrinkling on the compression-side facesheet. The progressive increase in mid-span displacement further reflects thermal softening and reduced structural stiffness.

Figure 4.

Post-failure images of sandwich composite structures with 0° self-sensing distal facesheets tested subjected to monotonic flexural tests at (a) 25°C, (b) 35°C, and (c) 45°C. An inset in (c) highlights surface wrinkling on the compression-side (loaded) facesheet.

Stress relaxation tests

Figure 5(a) and (b) presents the normalized stress relaxation behavior and corresponding FCR of the rGO-coated GFRP sandwich structures subjected to a constant displacement for three configurations: 0° fiber orientation with Nomex^® and aluminum honeycomb cores, and 90° orientation with a Nomex^®.

Figure 5.

Normalized load and FCR over time during stress relaxation for two different fiber orientations: (a) 0° with Nomex^® and Aluminum cores, and (b) 90° with Nomex^® core. Schematic illustrations of the proposed sensing mechanisms are shown in (c) for the 0° configuration and (d) for the 90° configuration.

In the 0° cases, Figure 5(a), both the 0-Nomex and 0-Al exhibit exponential stress decay, with greater relaxation levels observed in the Nomex^®, due to its viscoelastic nature. The FCR increases rapidly during the initial ∼30 min, then reaches a plateau. This initial increase, despite the constant displacement, is attributed to time-dependent microstructural changes, such as rGO flake reorientation, tunneling gap widening, or interfacial debonding, which reduce the connectivity of the rGO network, Figure 5(c). As the network stabilizes, the FCR approaches a plateau, though minor fluctuations persist, suggesting delayed local rearrangements rather than signal noise.^26,28

In contrast, the 90° Nomex^® configuration, Figure 5(b), shows a continuous decrease in both load and FCR, with no stabilization. In this case, the transverse fibers contribute little to load transfer, leaving the matrix response dominant. Matrix relaxation compacts the rGO network, improving inter-flake contact and reducing tunneling distances, which enhances conductivity over time. As shown in Figure 5(d), stress redistribution produces a denser, more conductive network. Unlike the 0° case, where early network increases the FCR, the 90° response exhibits a recovery mechanism governed by a matrix-driven conductivity enhancement.

Cyclic tests

Figure 6(a) and (b) presents the electromechanical response of self-sensing GFRP/Nomex^® sandwich composite structures subjected to cyclic flexural loading in 0° and 90° fiber orientations of the facesheet. Across 1000 load–unload cycles, both tracked the applied force, but orientation-dependent variations in signal stability and drift were evident.

Figure 6.

Electromechanical behavior of self-sensing GFRP/Nomex^® sandwich composite structures subjected to cyclic flexural load at 25°C, comparing the two different fiber orientations of the facesheet: (a) 0° and (b) 90°. The plots show force and FCR over 1000 loading–unloading cycles. Insets (i) and (ii) highlight the FCR response during early and late cycles, respectively, to assess baseline drift and sensing stability.

In the 0° case, early cycles showed a stable, periodic FCR with minimal baseline shift. The peak-to-peak response remained consistent, with the baseline increasing only slightly from ∼2.05% during early cycles, Figure 6(a) (i), to ∼2.15% in the final cycles, Figure 6(a) (ii), a drift of ∼0.10%.

In contrast, the 90° case exhibited greater irregularity initially. The baseline increased from ∼0.25%, Figure 6(b) (i), to ∼0.43% by the final cycles, Figure 6(b) (ii), a total drift of ∼0.18%. Despite this, the FCR signal stabilized towards the end, indicating network adaptation and reorganization.⁴¹

Both orientations also showed a slow decay in mean FCR, suggesting piezoresistive relaxation. The 0° decay was modest, consistent with reversible tunneling, whereas the 90° case exhibited a greater reduction, likely due to irreversible flake reorganization, interface recovery, or micro-gaps closure.⁴⁵ Similar viscoelastic-tunneling effects have been modeled in conductive polymer composites under cyclic deformation.²⁷

In comparison to earlier studies that primarily examined monotonic piezoresistive behavior of CNT- and graphene-based laminates,^15–23 the present work extends the analysis to include thermal effects, stress relaxation, and cyclic bending in rGO-coated GFRP sandwich structures. This broader characterization highlights the novelty of our approach in capturing both short-term and time-dependent electromechanical responses under flexural loading.

Furthermore, in contrast to conventional monitoring approaches that rely on external sensors, the present approach demonstrates how rGO-coated fabrics can transform sandwich composites into inherently self-sensing structures. This multifunctional capability not only enables integrated strain and damage sensing under thermal fluctuations and long-term loading but also reduces complexity by embedding sensing directly into the load-bearing material. Such advantages make rGO-coated facesheets attractive for aerospace components, as well as for marine and automotive sandwich structures where lightweight and real-time monitoring are equally critical.

Validation of the visco-piezoresistive and stress relaxation models

To capture the time-dependent electromechanical behavior of the sandwich structures, two models were employed: the visco-piezoresistive model (eq. (1)), applied to stress relaxation and cyclic tests, and the normalized stress model (eq. (2)), applied to stress relaxation only. Parameters were calibrated by fitting equations (1) and (2) to the experimental data using nonlinear least-squares regression. Figure 7(a)–(d) compares the experimental and fitted curves, with parameters listed in Tables 1 and 2. Both models show strong agreement with the experimental trends.

Figure 7.

Comparison between experimental and modeled normalized stress in the bottom facesheet and FCR for rGO-coated sandwich composites during stress relaxation: (a) 0° fiber orientation with Nomex^® core, (b) 0° fiber orientation with Aluminum core, (c) 90° fiber orientation with Nomex^® core, and (d) cyclic loading (mean FCR only).

Table 1.

Fitted parameters for the viscoelastic model (eq. (2)) applied to normalized stress during stress relaxation for different sandwich composite configurations.

	0-Nomex	0-Al	90-Nomex
$a$	$- 7.979$	$- 6.899$	$- 18.359$
$b$	$5.473$	$4.055$	$7.984$
$α$	$0.100$	$0.103$	$0.128$
$c$	$- 0.033$	$- 0.033$	$- 0.048$

Table 2.

Fitted parameters for the visco-piezoresistive model (eq. (1)) applied to FCR during stress relaxation and cyclic loading (mean FCR) data for different sandwich composite configurations.

	Stress relaxation			Mean cyclic
	0-Nomex	0-Al	90-Nomex	0-Nomex	90-Nomex
$a$	$1.336$	$0.358$	$- 48.527$	$0.504$	$0.583$
$b$	$- 1.045$	$- 0.349$	$48.572$	$- 0.396$	$- 0.689$
$α$	$0.126$	$0.560$	$0.001$	$0.137$	$0.230$
$c$	$- 0.001$	$0.001$	$0.057$	$- 0.004$	$- 0.002$

For stress relaxation, the 0-Nomex case showed a pronounced initial FCR response ( $a = 1.336$ ) followed by a gradual exponential decay ( $b = - 1.045$ , $α = 0.126$ ), consistent with visco-piezoresistive response, Figure 7(a). The normalized stress also delayed gradually ( $b = 5.473$ , $α = 0.100$ ), with a small negative drift ( $c = - 0.033$ ), reflecting delayed stress redistribution, due to viscoelasticity. In contrast, the 0-Al configuration exhibited faster, weaker relaxation in both stress and FCR, Figure 7(b), attributed to the elastic aluminum core, limiting time-dependent deformation.

For the 90-Nomex case, Figure 7(c), both stress and FCR relaxed continuously without stabilization. The parameters ( $a = - 48.527$ , $b = 48.572$ , $α = 0.001$ ) indicate a near-zero initial FCR and a very slow decay, while stress parameters ( $b = 7.984$ , $α = 0.128$ ) reflect a relatively faster mechanical relaxation. This highlights matrix-dominated deformation under transverse loading, which compacts the rGO network and enhances conductivity over time.

In cyclic tests, the model was fitted to the mean FCR, capturing the slow visco-piezoresistive evolution across cycles while filtering fluctuations, Figure 7(d). The 90-Nomex case showed stronger visco-piezoresistive effects than the 0° case, again due to matrix-dominated deformation and network compaction. The small drift term, $c$ , in both cases suggests largely reversible changes, without major network disruption.

Conclusions

This study investigated the time-dependent and thermo-mechanical piezoresistive response of self-sensing GFRP-based sandwich composite structures subjected to flexural loading, focusing on stress relaxation, cyclic, and thermomechanical loading conditions. The results clearly show that both fiber orientation and core material play a critical role in the electromechanical response of these self-sensing sandwich structures. When subjected to stress relaxation, distinct FCR trends were observed, an early increase and plateau in the 0° configurations, due to conductive network disruption, and a gradual decrease in the 90° configuration, driven by matrix relaxation and conductive network compaction. Cyclic tests revealed stable and reversible piezoresistive behavior, with orientation-dependent drift and relaxation characteristics. The 90° configuration exhibited a larger baseline shift and an FCR reduction, consistent with matrix-dominated sensing mechanisms.

A visco-piezoresistive model, analogous to the Burgers’ viscoelastic model, was used to fit both the relaxation and the cyclic FCR data. The model accurately captured the time-dependent electromechanical evolution, validating its ability to describe the interplay between mechanical viscoelasticity and visco-piezoresistivity.

Thermal effects further modulated the piezoresistive response. The rGO-coated laminates exhibited a negative temperature coefficient, and elevated temperatures resulted in a delayed onset of FCR and mechanical softening. Despite these changes, the sensing layer remained responsive and recoverable after failure, highlighting its ability to maintain sensing performance under varying conditions.

Overall, it is believed that the findings of this study advance the understanding of the long-term and temperature-sensitive electromechanical behavior of self-sensing sandwich structures, laying the foundation for improved modeling and integration of rGO-based sensors in SHM applications in the next-generation lightweight composite structures.

Footnotes

ORCID iDs

Noora Alahmed

Wesley J. Cantwell

Rehan Umer

Kamran A. Khan

Author Note

Rehan Umer: Division of Engineering Materials, Department of Management and Engineering (IEI), Linköping University, Sweden.

Funding

The authors disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by ASPIRE; Grant No. 8434000424/AARE20-124.

Declaration of conflicting interests

The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

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