Influence of Electrical Parameters in a Composite Wing Actuated by Shape Memory Alloys Wires: A Numerical–Experimental Study

Abstract

This study investigates the influence of electrical actuation parameters on the performance of a morphing composite aerodynamic profile actuated by Shape Memory Alloy (SMA) wires. A fully coupled electro-thermo-mechanical finite element model has been developed to simulate the transient response of NiTi SMA, capturing the nonlinear interplay between temperature evolution, phase transformation, and mechanical deformation under Joule heating. The model incorporates phase-dependent material properties, heat effects, and geometric constraints, enabling accurate prediction of actuation dynamics. To validate the model, a morphing spoiler prototype has been fabricated using high-performance additive manufacturing with a carbon fibre-reinforced polymer. The SMA wires have been pretensioned and electrically actuated at different current levels (3 A and 6 A), and the resulting deformation has been recorded through video analysis with embedded timers. Experimental measurements confirmed the model’s ability to predict both actuation time and displacement, with maximum deflections of 33 mm and 40 mm corresponding to different current inputs. This integrated approach demonstrates an efficient and compact solution for active aerodynamic surfaces without the need for mechanical linkages, enabling future developments in adaptive structures for automotive and aerospace applications.

1. Introduction

Shape Memory Alloys (SMAs), particularly nickel–titanium (NiTi) alloys, have emerged as key materials for smart actuators due to their ability to undergo large, reversible deformations driven by thermally induced martensitic–austenitic phase transformations [1]. This thermo-mechanical behaviour allows SMAs to convert electrical energy into mechanical work in a compact, silent, and lightweight configuration, making them suitable for a wide range of applications, including aerospace morphing surfaces [2], biomedical tools [3], and adaptive structures [4,5].

Most SMA-based systems rely on antagonistic wire configurations or biassing mechanisms such as springs and preloaded elastic components to enable cyclic actuation and shape recovery [6,7]. While effective, these designs introduce added weight, mechanical complexity, and reduced reliability, particularly in miniaturized systems or additively manufactured morphing components. Antagonistic SMA setups, for instance, require symmetric thermal control and dual actuation channels, increasing power demand and thermal inertia [8].

Recent work has explored SMA-driven morphing concepts with embedded or surface-integrated wire actuators. Barbarino et al. [9] presented a trailing edge morphing concept actuated by antagonistic SMA wires embedded within a composite skin, demonstrating effective bidirectional bending. While this setup allowed for smooth deformation and shape retention, it required precise thermal management and doubled the electrical control effort due to the opposing wire system. More recently, Riccio et al. [5] proposed a bistable SMA-driven morphing spoiler for adaptive automotive aerodynamics, while Jiannan et al. [2] presented a flexible multi-mode morphing wing using SMA wires for directionally controlled deformation. Moreover, more recent developments have explored embedding SMA wires into elastomeric matrices or soft composites, where the elastic recovery of the host material substitutes the traditional bias mechanism [10]. These solutions achieve a higher level of integration and passive recovery but often at the cost of reduced stroke, slower response times, and fabrication challenges due to the need for co-curing and material compatibility. Other approaches include multi-material or bistable structures, frequently enabled by additive manufacturing, which rely on complex geometry or internal mechanical instabilities to amplify motion and store elastic energy [11]. While structurally innovative, these systems may still require external actuation or reset mechanisms, limiting their operational autonomy.

At the modelling and experimental level, several contributions exist but often with limitations. Rodinò et al. [12] focused on automated thermo-mechanical/electrical characterization of NiTi wires, while Tshikwand et al. [13] developed a coupled FEM model for micro-scale actuators. Puente-Córdova et al. [14] examined NiTi coil springs under electrical loads (2.5 A), Sciberras et al. [15] applied fluid–structure interaction to MEMS devices, and Zhang et al. [16] proposed a fluid-cooled NiTi artificial muscle to enhance frequency. Despite demonstrating substantial improvements in thermal responsiveness, their model does not implement a fully coupled finite element electro-thermo-mechanical simulation, nor does it simulate deformation under variable electrical currents in structural profiles typical of morphing systems.

The present study addresses these limitations by proposing a fully coupled FEM-based electro-thermo-mechanical model tailored for a morphing aerodynamic profile actuated by NiTi SMA wires.

In contrast to the existing approaches, the research proposes a novel SMA-actuated morphing profile that addresses these limitations by eliminating the need for any external mechanical actuators or biassing elements. The system consists of an additively manufactured structure integrated with a single SMA wire. Shape change is induced exclusively via electrically controlled Joule heating. This results in a self-contained, low-complexity actuation system that leverages the intrinsic properties of the SMA and the host structure to perform reversible deformations with minimal hardware.

To evaluate the dynamic behaviour and performance of the system, numerical simulations and experimental tests under two actuation regimes (6 A and 3 A) are conducted. These two input levels allow us to examine the effect of thermal power on response speed and the actuation amplitude. The results provide insights into the trade-offs between energy input and actuation performance and validate the feasibility of simplified SMA-based morphing structures that require only current control for operation.

In Section 2, the theoretical background of the coupled analysis is presented. Section 3 describes the conceptual design of the morphing spoiler. Section 4 compares the numerical and experimental results. Conclusions are provided in Section 5.

2. Theoretical Background

The thermo-mechanical behaviour of SMA materials is governed by a complex interplay of thermal, electrical, and structural phenomena, primarily driven by the martensitic-austenitic phase transformation. When heated above the austenite start temperature, SMA wires contract as they transition to the austenitic phase, and upon cooling, they can return to their original shape due to the pseudoelastic or shape memory effect.

The phase transformation temperatures, specifically the austenite start (As) and finish (Af), as well as martensite start (Ms) and finish (Mf), are important in defining the actuation range of SMA components. These temperatures are highly sensitive to manufacturing history, composition, and mechanical prestrain. In the present work, the SMA wires have been pretensioned prior to activation, thereby modifying the transformation stresses and slightly shifting the transformation temperatures.

To accurately predict the transient response of SMA actuators, a fully coupled electro-thermo-mechanical modelling approach is required. This framework must account for the following factors:

Electrical conduction. which defines the Joule heating input as a function of current, geometry, and temperature-dependent resistivity.

Thermal diffusion, which governs the evolution of the internal temperature field, considering conduction, convection, and radiative losses.

Mechanical response, including thermally induced expansion, transformation strain, and the associated stress–strain–temperature hysteresis.

Accurate modelling of SMA actuators requires considering the strong coupling between electrical, thermal, and mechanical fields. Joule heating from applied current drives the martensite–austenite transformation, generating contraction and deformation. In complex systems with non-uniform heating, nonlinear geometry, or dynamic reconfiguration (e.g., morphing wings, adaptive robotics), simplified models fail to capture critical metrics such as actuation time, displacement, and efficiency. Hence, fully coupled electro-thermo-mechanical models are essential for predicting transient responses, optimizing energy use, and supporting sensor-based control strategies.

Several modelling strategies have been proposed in the literature to capture the complex behaviour of SMAs. Simplified one-dimensional lumped-parameter approaches often represent the material as a resistive element with temperature-dependent resistivity, combining classical heat transfer relations with phase transformation kinetics [16,17,18,19]. Although computationally efficient and useful for preliminary design, such models overlook spatial gradients and nonlinear effects intrinsic to SMA actuation. At the same time, electrical parameters have been shown to play a decisive role in shaping both the preparation and functional response of metallic materials under electrothermal coupling. Recent studies confirm that controlled electrical inputs can profoundly influence microstructural evolution, mechanical performance, and phase transformation behaviour, thus opening new opportunities for material optimization.

For instance, the work of [20] reported the effect of cryogenic and electrothermal coupling treatment on Ti6Al4V alloy, highlighting how electrical parameters directly impact both microstructural refinement and mechanical performance. Similarly, Ref. [21] investigated the influence of low-density DC electric fields on cast TC4 alloy, providing a detailed analysis of microstructural evolution, property modification, and associated toughening mechanisms.

A critical challenge in such modelling is the presence of a strong feedback loop: mechanical deformation alters the electrical resistance of the SMA, which in turn modifies the local Joule heating rate. For systems operating with variable current levels, as in the case of the present study, which compares 3 A and 6 A actuation, a dynamic model that accounts for nonlinear thermal diffusion and phase-dependent resistivity is essential to predict actuation time, maximum displacement, and recovery behaviour.

To ensure accurate predictions, the electro-thermal properties of the SMA material have been experimentally calibrated. Direct resistance measurements under varying temperatures have been conducted to define the temperature-dependent electrical resistivity. These calibrated parameters have then been introduced into the material subroutine used in the FEM model, ensuring a strong match between simulation and experimental response. Nickel–titanium (NiTi) wires have been used due to their well-established shape memory behaviour and good electro-thermal efficiency. The key material parameters, including transformation temperatures, heat flow and Young’s modulus, have been characterized experimentally and are listed in

Table 1. Nickel–titanium (NiTiNOL) thermo-mechanical–electrical properties [20,23].

NiTiNOL
Austenite Elastic Modulus  ${\mathrm{E}}_{\mathrm{A}}$ (MPa)	115,870
Martensite Elastic Modulus ${\mathrm{E}}_{\mathrm{M}}$ (MPa)	51,870
Austenite Poisson’s ratio ${\mathsf{\upsilon }}_{\mathrm{A}}$	0.33
Martensite Poisson’s ratio ${\mathsf{\upsilon }}_{\mathrm{M}}$	0.33
Residual strain ${\mathsf{\epsilon }}_{\mathrm{l}}$	0.067
${\mathrm{C}}_{\mathrm{A}}\left[\mathrm{M}\mathrm{P}\mathrm{a}/\mathrm{K}\right]$	8
${\mathrm{C}}_{\mathrm{M}}\left[\mathrm{M}\mathrm{P}\mathrm{a}/\mathrm{K}\right]$	8
Martensite finish temperature ${\mathrm{M}}_{\mathrm{f}}$ (K)	303
Martensite start temperature ${\mathrm{M}}_{\mathrm{s}}$ (K)	338
Austenite start temperature ${\mathrm{A}}_{\mathrm{s}}$ (K)	328
Austenite finish temperature ${\mathrm{A}}_{\mathrm{f}}$ (K)	381
Critical transformation start stress ${\mathsf{\sigma }}_{\mathrm{s}\mathrm{c}\mathrm{r}}$ (MPa)	15
Critical transformation finish stress ${\mathsf{\sigma }}_{\mathrm{f}\mathrm{c}\mathrm{r}}$ (MPa)	100
Martensite thermal expansion coeff. ${\mathsf{\alpha }}_{\mathrm{M}}$ (K−1)	2.2 × 10−6
Austenite thermal expansion coeff. ${\mathsf{\alpha }}_{\mathrm{A}}$ (K−1)	2.2 × 10−6
Martensite Thermal conductivity (W/mmK)	0.0085
Martensite Electric conductivity (1/Ωmm)	1250
Convective heat transfer coefficient (W/mm2K)	8.19 × 10−5
Austenite Thermal conductivity (W/mmK)	0.018
Austenite Electric conductivity (1/Ωmm)	1000
Convective heat transfer coefficient (W/mm2K)	8.19 × 10−5

. The experimental study of these material properties to actuation performance has been previously investigated in [22,23], where the SMA element has been tested in its austenite and martensite phases using a controlled heating system. These previous analyses confirm that moderate variations in material parameters may slightly affect local stress or thermal gradients but do not significantly influence the overall actuation dynamics, supporting the reliability of the numerical model.

To simulate the behaviour of the SMA-actuated profile, a multiphysics model has been developed, incorporating the following coupled fields:

2.1. Electrical Model—Joule Heating

Joule heating is modelled based on the power dissipation in the wire:

$$Q_{Joule}=I^{2}R={\displaystyle \frac{I^2 {\rho }_{c}L}{A}}$$

(1)

$I$ is the applied current;

$L$ is the wire length;

$A$ is the cross-sectional area of the wire.

2.2. Thermal Model

Heat transfer within the SMA wire and to the surrounding medium has been modelled using the transient heat equation:

$$\rho c_p{\displaystyle \frac{\partial T}{\partial t}}=\nabla \cdot (\mathrm{k}\nabla \mathrm{T})+{\mathrm{Q}}_{Joule}-{\mathrm{Q}}_{loss}$$

(2)

Heat loss ${\mathrm{Q}}_{loss}$ includes convection, modelled as follows:

$${\mathrm{Q}}_{loss}=h(T-T_{\infty })$$

(3)

where

$h$ is the convective heat transfer coefficient,

$T_{\infty }$ is the ambient temperature.

2.3. Mechanical Model—SMA Constitutive Law

The SMA behaviour has been modelled using a phenomenological approach and a custom User Subrotuine MATerial (UMAT) [24], which captures both the elastic and transformation-induced strains:

$$ϵ={\displaystyle \frac{\sigma }{E}}+{\epsilon }_l\xi$$

(4)

where

$\sigma$ is the stress,

$E$ is the Young’s modulus (temperature-dependent),

${ϵ}_l$ is the maximum transformation strain,

$\xi \in \left[\mathrm{0,1}\right]$ is the martensitic volume fraction.

The evolution of $\xi$ is governed by transformation kinetics, defined by thermally driven forward and reverse transformations:

$$\xi =f(T,\sigma )$$

(5)

Although the model does not include microstructural evolution or internal damping mechanisms, it captures with sufficient accuracy the macroscopic response of the SMA actuator, particularly in terms of displacement amplitude and actuation time. The chosen approach offers a good trade-off between computational efficiency and predictive fidelity, making it suitable not only for validation purposes but also for iterative design and system-level integration of SMA-based morphing mechanisms.

2.4. Conceptual Design

The proposed solution addresses the common limitations of traditional SMA-actuated morphing systems, such as increased weight, architectural complexity, and reduced reliability caused by external bias mechanisms (e.g., springs or antagonistic actuators). By eliminating the need for additional mechanical components and relying solely on current-controlled heating of strategically designed SMA wire configurations, this approach significantly reduces the overall system mass and volume. Furthermore, the integration of a fully coupled electro-thermo-mechanical model allows for precise prediction and optimization of actuation time and deformation amplitude, enhancing control accuracy and energy efficiency.

To investigate the impact of current amplitude on the actuation dynamics, simulations and experiments were conducted under two input regimes:

Case A: High-current actuation at 6 A.

Case B: Low-current actuation at 3 A.

The purpose of this study is to validate a numerical model capable of accurately predicting the thermo-electro-mechanical behaviour of the SMA-actuated morphing profile. The model aims to capture significant differences in temperature rise rates and actuation times under varying current inputs. Validation will be performed by comparing numerical predictions with experimental data, where optical tracking of the profile deformation provides direct measurement of response times. Building on the validation of the numerical model for thermo-electro-mechanical behaviour, the study advances toward a system-level application by integrating the validated SMA actuation strategy into a complete morphing spoiler design. The insights gained from the numerical–experimental comparison, particularly regarding temperature rise dynamics and actuation timing under different current inputs, serve as the foundation for developing a reliable simulation of the full-scale system. Leveraging this model, a spoiler featuring distributed actuation and minimal mechanical complexity has been designed, offering enhanced spatial efficiency and weight reduction. This transition from material-level validation to component-level implementation enables a seamless integration of SMA actuation directly onto the internal surface of the aerodynamic profile, eliminating the need for traditional transmission mechanisms and maximizing design compactness. Based on comprehensive numerical thermal and mechanical validation [5,24], a detailed numerical model of a spoiler has been developed, demonstrating its capability to achieve significant rotation at the trailing edge. This designed solution proves to be considerably more efficient than earlier configurations in terms of space and weight requirements, as the actuator is directly bonded to the internal surface of the spoiler and does not rely on any mechanical transmission or motion mechanism for activation. An additional aspect to consider for practical implementation is the long-term cyclic performance of the NiTi SMA wires. Although the present study focuses on the validation of the numerical model and the actuation dynamics under different current inputs, it is well known that repeated thermo-mechanical loading can induce material fatigue, potentially affecting actuation amplitude and response time over extended use. Literature reports that the fatigue life of NiTi wires strongly depends on strain amplitude, temperature, and current input, with stable actuation cycles ranging from 10³ to 10⁵ for moderate strains [25,26,27]. In the present work, the numerical routine does not account for fatigue effects, and simulations carried out for multiple cycles show no degradation, as mechanical property variations due to fatigue are not implemented. Nevertheless, this limitation is acknowledged, and future work will include experimental fatigue testing and model refinement to incorporate degradation effects. Recognizing these practical boundaries ensures that the proposed SMA-actuated spoiler design maintains reliability while guiding subsequent investigations on the cyclic durability of the integrated actuation system.

The aerodynamic profile selected for this investigation is the NACA0012 airfoil, specifically chosen for its suitability to fabrication via Fused Filament Fabrication (FFF) additive manufacturing technology. With the rapid advancement of Industry 4.0, Additive Manufacturing has revolutionized the design and production of aerospace structures [28], which are inherently complex due to their need to withstand both structural and aerodynamic loads. Traditionally, these components have been designed using shell-based configurations where distinct segments serve specific structural roles: longitudinal and transverse reinforcements distribute loads, while the outer skin reduces drag and enhances aerodynamic performance. This conventional methodology involves separate design, manufacturing, and subsequent assembly through riveting, increasing complexity and weight. However, ongoing technological progress is driving a paradigm shift toward more cost-effective and innovative methods, prioritizing lightweight, high-performance solutions and streamlined manufacturing [29]. Additive Manufacturing is at the forefront of this shift, enabling the integration of advanced materials and complex geometries into a single multifunctional component. In particular, the use of internal infill structures in 3D printing redefines load-bearing concepts by replacing discrete beams and shells with a continuous, optimized internal framework [30], termed a collaborative volume, thus eliminating the need for separate structural elements and enabling a new class of lightweight, multifunctional aerospace components.

Various infill configurations can be tailored to achieve an optimized internal architecture. For instance, different geometric cell structures, such as honeycomb or quadrangular patterns, combined with varying infill densities, directly influence mass reduction and mechanical performance. Experimental data indicates that an infill density of 50% already yields substantial weight savings compared to a fully solid structure. Further optimization, with an infill density reduced to 20%, can achieve up to a 38% reduction in mass while maintaining structural integrity (Figure 1).

Beyond material efficiency, this methodology provides flexibility in design, allowing structures to be tailored to specific operational requirements. In AM component design, the selection of infill type and density is critical, as it directly impacts mechanical properties, structural behaviour, and overall performance. The infill pattern dictates material distribution, affecting strength and rigidity, while the infill percentage determines weight and load-bearing capacity [31].

In this study, the spoiler used for numerical analysis is a NACA0012 (Figure 2) with a chord of 500 mm. The thickness is 1.5 mm and the component has been designed for FFF technology.

Two structural elements have been added in the additive configuration and have been produced with an infill structure (20%—quadrangular patterns). A tolerance of 1.2 mm [32] has been used to avoid the condition of no-sliding (Figure 2).

To improve the system’s performance, it is proposed to evaluate the direct application of SMA wires (FLEXINOL STD-020-90), strategically placed inside an aerodynamic profile (Figure 3). This solution aims to optimize the final displacement of the trailing edge, taking advantage of the unique properties of Shape Memory Alloys to achieve wider and more controlled movements, while maintaining a compact system that is easy to install. To support this proposal, a numerical analysis has been carried out based on the application of an electrical load to SMA wires.

The electrical load has been generated by assuming a current of 6 A and 3 A, which allows the activation and control of the deformation of the SMA wires.

3. Results

Numerical Results

The numerical model developed in this study employs a fully coupled electro-thermo-mechanical framework to accurately simulate the complex behaviour of the SMA-actuated morphing profile. The electrical domain is modelled by solving the Joule heating problem through the electrical conduction equation, accounting for the temperature-dependent electrical resistivity of the SMA material. This allows precise prediction of local heat generation when an electric current passes through the wire actuator. The thermal field thus obtained governs the phase kinetics, which are linked to the mechanical response via constitutive relations. The mechanical behaviour is described using a thermoelastic constitutive model [20] that captures the strain induced by phase transformation, thermal expansion, and external loading conditions. Material properties such as transformation temperatures, specific heat capacity, thermal conductivity, Young’s modulus, and transformation strain are characterized experimentally and incorporated into the model to enhance predictive accuracy (Table 1).

The coupled solver iteratively exchanges information between the electrical, thermal, and mechanical fields at each time step, allowing the simulation to capture the strong interdependencies and nonlinearities inherent in SMA actuation. This integrated approach enables the prediction of actuation time, deformation amplitude, temperature evolution, and the influence of thermal lag and hysteresis effects, providing a comprehensive tool for optimizing the design and control of SMA-driven morphing structures.

The actuation cycle of the SMA wire is numerically modelled by simulating the full thermo-electro-mechanical interaction responsible for shape recovery under thermal excitation. Initially, the wire is assumed to be in its martensitic state and mechanically pre-strained, representing the extended (deactivated) configuration. Actuation is triggered by applying an electrical current, which induces internal heat generation via Joule effect. Electrical conductivity is defined as a function of temperature and phase fraction to capture the resistivity drop during the austenitic transformation. The resulting thermal field is obtained by solving the transient heat conduction equation. As the temperature exceeds the austenite start temperature, the material undergoes a solid-state phase transformation, and a thermally induced contraction is produced, generating recovery forces on the surrounding structure. The mechanical response is governed by a constitutive law that incorporates both thermal expansion and transformation strain, enabling the accurate reproduction of deformation dynamics and internal stress evolution.

In details, in the initial configuration, the SMA wire is assumed to be in the fully martensitic phase and is mechanically pretensioned by 8 mm prior to activation. This pre-strain condition is essential to enable recovery stress development during heating and to ensure a measurable contraction stroke upon phase transformation. This preloaded state is introduced as an initial mechanical condition in the numerical model, influencing both the internal stress field and the boundary reaction forces during subsequent heating and cooling phases.

A custom FEM implementation has been used within a commercial multiphysics environment, where the SMA wire has been modelled as 3D element with coupled Joule heating and thermo-mechanical behaviour. The geometry of the morphing profile has been discretized using hexahedral elements, and the boundary conditions have been applied to reproduce the same constraints observed in the experimental prototype. Contact interfaces between SMA wires and additive structure have been assumed bonded, ensuring effective load transfer (Figure 4).

Electrical excitation is applied as a transient current input, with two distinct amplitude levels considered: 3 A and 6 A. These values are imposed as boundary conditions in the coupled electro-thermal model, which resolves the time-dependent evolution of the temperature field due to Joule heating. The transient thermal response reveals a significantly faster temperature rise under 6 A excitation, with the wire reaching the austenite start temperature in approximately 2.24 s (Figure 5a), compared to over 9.64 s for the 3 A case (Figure 5b).

The numerical simulations provided detailed insight into the thermo-mechanical response of the SMA-based actuation system. The computed displacement profile as a function of time closely follows the temperature evolution within the SMA wire. Initially, as the electrical current is applied, the temperature increases due to Joule heating, but the displacement remains negligible until the local temperature exceeds the austenite start temperature (As). At this threshold, the phase transformation from martensite to austenite initiates, resulting in a rapid increase in displacement (Figure 6a). This nonlinear transition is clearly visible in the simulation output, where a sharp change in the displacement–temperature curve coincides with the As value. For both current inputs (3 A and 6 A), the simulation confirms that the actuation mechanism is activated only once the SMA material reaches the critical transformation temperature (Figure 6b).

The mechanical response of the SMA actuator, as predicted by the coupled electro-thermo-mechanical model, shows a clear dependence on the applied current level. When a 6 A current is applied, the wire undergoes a rapid phase transformation and generates sufficient recovery force to induce a maximum trailing-edge displacement of approximately 40 mm (Figure 7a). In contrast, the 3 A actuation results in a slower transformation rate and a reduced maximum displacement of about 33 mm (Figure 7b). This difference is primarily attributed to the lower internal heat generation at 3 A, which delays the austenitic transformation and limits the extent of contraction before thermal equilibrium is reached. The simulation also confirms that the final displacement is influenced not only by temperature but also by the transformation kinetics and thermal losses, reinforcing the importance of current amplitude in shaping the actuator’s performance envelope.

However, variations in environmental conditions or material properties may slightly affect these values. The numerical results, combined with the simulation of the dynamic behaviour of the SMA wires within the profile, provide a clear view of the potential of this solution. In particular, the analysis helps to quantify the temporal response and optimize the load distribution to maximize the system’s effectiveness in practical applications.

4. Experimental Results

To validate the numerical predictions, an experimental setup has been developed replicating the same geometric and boundary conditions implemented in the simulation. The physical prototype consists of a 3D-printed morphing spoiler fabricated using Fused Filament Fabrication (FFF) with a carbon fibre-reinforced thermoplastic, based on the NACA0012 airfoil geometry with a length of 75 mm.

The morphing spoiler prototype has been fabricated using the Roboze ARGO 500 (Bari, Italy), an industrial-grade Fused Filament Fabrication (FFF) 3D printer capable of processing high-performance thermoplastics with excellent dimensional accuracy (Figure 8). The selected material is a carbon fibre-reinforced polymer, chosen for its favourable strength-to-weight ratio and thermal stability [31]. Prior to printing, the CAD model of the spoiler has been carefully prepared through a dedicated slicing process, where layer thickness, infill pattern, and support structures have been optimized to ensure both mechanical performance and surface quality. Particular attention has been paid to dimensional tolerances to guarantee proper fit and structural integration. The final printed component underwent a post-processing phase, including support removal and dimensional inspection using a digital calliper, which confirmed that all critical features were within the acceptable tolerance range defined in the design specifications.

Two NiTi Shape Memory Alloy (SMA) wires, with a diameter of 0.508 mm and austenite finish temperature of approximately 108 °C, have been bonded along the inner surface of the spoiler using high-temperature epoxy adhesive. The wire has been pretensioned by 8 mm before being fixed in place, reproducing the initial strain conditions applied in the numerical model (Figure 9). Electrical activation has been provided by a programmable DC current generator capable of supplying constant current levels of 3 A and 6 A. The experimental campaign has been designed to replicate the transient actuation process simulated numerically, enabling a direct comparison in terms of activation time, peak displacement, and thermal evolution.

The experimental validation focused on assessing the dynamic response of the SMA-actuated morphing spoiler in terms of actuation time and displacement amplitude under different electrical inputs. Two current levels, 3 A and 6 A, have been applied in transient mode. Results demonstrated a clear correlation between input current and actuation performance. At 6 A, the system reached its maximum displacement of approximately 38 mm in under 2.54 s (Figure 10a), whereas at 3 A, the actuation was slower and less pronounced, achieving a peak displacement of 29 mm in roughly 11.14 s (Figure 10b). These outcomes are consistent with the numerical predictions and confirm the strong influence of Joule heating on the phase transformation rate and deformation dynamics of the SMA wires. Moreover, no signs of instability or mechanical backlash have been observed during repeated actuation cycles, indicating reliable integration between the printed structure and the actuation system.

The reliability and reproducibility of the measured displacements have been systematically assessed through repeated measurements for both current levels. For the 6 A input, three independent measurements have been performed, yielding displacements of 40 mm, 38 mm, and 39 mm, resulting in a mean value of 39 mm and a standard error of approximately 0.58 mm. Similarly, for the 3 A input, four measurements produced values of 27 mm, 28 mm, 29 mm, and 28 mm, corresponding to a mean displacement of 28 mm with a standard error of about 0.41 mm. The small standard errors observed indicate high consistency across repeated measurements and minimal variability, confirming the reliability of the reported mean values. These results demonstrate that the experimental setup provides stable and reproducible measurements of SMA-actuated displacements, with a precision on the order of 1 mm. This level of accuracy is sufficient to capture the main trends in actuation behaviour and allows for a meaningful comparison between different current inputs.

High-resolution video recordings have been acquired throughout the experimental tests to accurately monitor the shape evolution of the morphing profile during actuation for 6A test (Figure 11a) and for 3A test (Figure 11b). The recordings have been performed using a calibrated optical setup at a fixed frame rate, ensuring consistent time resolution across different tests. By performing a frame-by-frame analysis, the time required for the complete shape transition has been determined for each current input scenario. To enhance measurement accuracy, a digital timer was embedded directly into the video frames, providing a synchronized and continuous time reference throughout the actuation sequence. This approach enabled a detailed evaluation of the actuation dynamics, including the onset of motion, the duration of deformation, and the time required to reach the actuated configuration. The visual data have been further processed using image tracking software to extract quantitative displacement-time curves, which were subsequently compared with the numerical predictions. This methodology provided an effective and non-intrusive means of validating the transient behaviour of the SMA-actuated system.

A summary of the sensitivity analysis regarding the electrical current input is provided in

Table 2. Comparison between numerical predictions and experimental results for SMA actuation under two current inputs (6 A and 3 A).

		Case A (6 A)	Case B (3 A)
Numerical results	Actuation time [s]	2.44	9.64
	Max displacement [mm]	40.3	33.1
Experimental tests	Actuation time [s]	2.54	11.14
	Max displacement [mm]	38	29

. For the higher current level (6 A), the numerical model predicted an actuation time of 2.44 s, closely matching the experimental result of 2.54 s, with a maximum displacement of 40.3 mm versus 38 mm measured experimentally (≈6% difference). For the lower current level (3 A), the actuation time increased to 9.64 s (experimental 11.14 s, ≈14% difference), and the maximum displacement decreased to 33.1 mm (experimental 29 mm, ≈14% difference). It is important to note that halving the applied current does not lead to a proportional 50% reduction in displacement. This behaviour stems from the nonlinear coupling between electrical heating, temperature-dependent phase transformation and intrinsic mechanical contraction in SMA materials. At lower currents, the rate of temperature increase is slower, which delays the onset and progression of the austenitic transformation. However, once the transformation has started, a significant portion of the SMA still reaches complete transformation, so the total displacement does not increase linearly with current. In addition, thermal losses and the nonlinear dependence of resistivity and phase fraction on temperature further contribute to this discrepancy. These results confirm that the applied current is the dominant factor influencing the actuation dynamics, while all other boundary conditions and material parameters were kept constant. The good agreement between the numerical and experimental data demonstrates the robustness of the proposed model in predicting SMA actuation under variable electrical loads and highlights the nonlinear sensitivity of the displacement to the input current.

Table 3. Comparative overview of SMA-based morphing actuators in the recent literature.

Study	SMA Type	Actuation Mechanism	Applied Current	Max Displacement [mm]	Actuation Time [s]	Notes
Present Work	NiTi wire	Direct current-controlled heating	3 A/6 A	29–40	2.54–11.14	Compact system without external mechanical components; fully coupled electro-thermo-mechanical FEM model validated
Lee & Lee, 2023 [33]	Braided SMA wire	Torsional actuation in PDMS matrix	1–3 A	10–20	2–5	Soft actuators for adaptive wings; torsional deformation
Kim et al., 2023 [34]	Various SMAs	Direct heating	2–5 A	15–30	3–7	Review of SMA material properties and applications
Jia et al., 2025 [35]	SMA wire	Direct heating	4–6 A	20–35	4–8	Actuators for bionic deformable wings; aerospace applications

provides a comparative overview of recent SMA-based morphing actuator studies, highlighting key parameters such as SMA type, actuation mechanism, applied current, maximum displacement, and actuation time. The present work demonstrates clear advantages over previously reported configurations by achieving larger displacements (up to 40 mm) while maintaining compactness and eliminating external mechanical components. Furthermore, the dual-current approach (3 A and 6 A) enables controlled variation in actuation speed and amplitude, which has been validated experimentally and through a fully coupled electro-thermo-mechanical FEM model. Compared to soft actuators, torsional systems, and microscopic devices, the proposed strategy offers superior predictive accuracy, energy efficiency, and system integration potential. Overall, this comparison emphasizes the practical and scalable benefits of the current-controlled SMA actuation methodology for aerospace morphing applications.

5. Conclusions

This study presents the design, numerical modelling, fabrication, and experimental validation of a novel SMA-actuated morphing spoiler, integrating a fully coupled electro-thermo-mechanical simulation framework with high-precision additive manufacturing. The developed system demonstrates the feasibility of achieving significant trailing-edge displacement using embedded NiTi SMA wires directly bonded to the inner surface of a carbon-fibre-reinforced polymer structure.

The detailed finite element model, incorporating temperature-dependent material properties, phase transformation kinetics, and Joule heating effects, accurately predicted transient actuation behaviour under different electrical loads (3 A and 6 A). The simulations closely matched the experimental measurements, showing strong agreement in actuation onset, displacement amplitude (up to 40 mm), and transformation temperatures. From an engineering perspective, the proposed solution offers several advantages: it eliminates the need for mechanical transmissions, reduces weight and system complexity, enables distributed and surface-conformal actuation, and provides a compact, scalable, and energy-efficient SMA actuation strategy. These features make the system highly suitable for aerospace and automotive applications where lightweight, reliable, and precise morphing structures are required. Regarding future improvement directions, the validated framework enables further studies on variable geometry optimization, active control strategies, energy consumption minimization, and long-term fatigue performance assessment. Overall, this work establishes a clear pathway for the practical implementation of lightweight, high-performance morphing structures using SMA actuation.