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Article

Exploring Water-Induced Helical Deformation Mechanism of 4D Printed Biomimetic Actuator for Narrow Lumen

by
Che Zhao
1,†,
Lei Duan
1,†,
Hongliang Hua
1 and
Jifeng Zhang
2,*
1
School of Aeronautics and Mechanical Engineering, Changzhou Institute of Technology, Changzhou 213032, China
2
College of Mechanical and Electrical Engineering, Changchun University of Science and Technology, Changchun 130022, China
*
Author to whom correspondence should be addressed.
†
These authors contributed equally to this work.
Machines 2025, 13(1), 31; https://doi.org/10.3390/machines13010031
Submission received: 10 December 2024 / Revised: 2 January 2025 / Accepted: 5 January 2025 / Published: 6 January 2025
(This article belongs to the Special Issue Advances in 4D Printing Technology)
Browse Figures
Versions Notes

Abstract

:
To address the issues of limited adaptability and low spatial utilization in traditional rigid actuators, a biomimetic actuator with water-induced helical deformation functionality was designed. This actuator is capable of adaptive gripping and retrieval of objects in a narrow lumen. A numerical model was established to analyze its helical deformation mechanism, and the helical deformation characteristics of the actuator were calculated under different structural parameters. Based on four-dimensional (4D) printing technology, which integrates three-dimensional printed structures with responsive materials, experimental samples of biomimetic actuators were fabricated by combining thermoplastic polyurethane fiber scaffolds with water-absorbing polyurethane rubbers. By comparing the simulation results with the experimental data, the numerical model was corrected, providing theoretical guidance for the structural optimization design of the actuator. The experiment shows that the biomimetic actuator can act as a gripper to capture a small target in a lumen less than 5 mm in diameter. This research provides a theoretical and technical foundation for the development of specialized actuators aimed at narrow spaces.

1. Introduction

Actuators are essential in robotics for manipulating objects and are commonly employed in settings like industrial production lines, logistics hubs, and laboratories [1,2]. However, traditional rigid actuators struggle as grippers in specialized environments like narrow channels in precision instruments or ducts in the human body [3,4]. The rigid components, such as pumps, fasteners, connectors, and electronic elements, limit the miniaturization and flexibility of the actuators [5,6]. Moreover, the deformation modes of most actuators, which mimic finger bending, result in low space efficiency, making them ineffective in narrow pipes or gaps [7,8]. Thus, there is an urgent need to develop new actuators with high spatial efficiency and excellent adaptability.
Biomimetics has become an important source of innovation, offering new ideas to address many technological challenges [9,10,11]. Although the functional capabilities of plants are limited in scope, they still exhibit remarkable capabilities comparable to those of animals. For example, the seed dispersal organs of plants are mainly composed of polymers, such as cellulose, hemicellulose, and lignin [12], and lack complex neural–muscular–skeletal systems. However, organs such as pinecone scales [13], wheat awns [14], and Geraniaceae seed awns [15] undergo deformation in response to humidity, facilitating seed protection, dispersal, and transport. Reyssat et al. [16] established a mathematical model based on the theory of thermally induced bimetals to explain the bending deformation mechanism in plant tissues. Guided by this model, researchers have developed various biomimetic actuators. Li et al. [17] developed a photothermal-responsive gradient-crosslinked hydrogel actuator with excellent mechanical properties that can be used as a mechanical gripper. Lin et al. [18] developed a humidity-responsive film actuator that achieved rapid rolling through bending deformation. Li et al. [19] designed a biomimetic actuator with a heterogeneous laminated bilayer structure, enabling controllable bending deformation in response to temperature changes. Zhao et al. [20] designed a hydrogel actuator with differentiated hydrogen bond networks, using the expansion pressure gradient inside the hydrogel to achieve various sequential bending deformations. Although the biomimetic actuators overcome the limitations of rigid components and achieve miniaturization, they are still constrained by the low space efficiency associated with bending deformation.
Snir et al. [21] demonstrated from an entropy perspective that helical structures offer significant advantages in spatial efficiency. Thereafter, Hu et al. [22] employed a bilayer hydrogel structure to induce helical deformation in a biomimetic actuator under water, enabling it to adapt to tubular tissues of varying curvatures. Similarly, Shi et al. [23] developed a cellulose vascular stent that undergoes helical expansion in response to water or alcohol stimuli. However, despite these advancements, these biomimetic actuators can only modify their deformation characteristics by altering the overall moment of inertia, which limits their practicality as grippers in confined spaces.
Four-dimensional printing is an advanced manufacturing technique that combines traditional three-dimensional printing with materials that can change shape or properties in response to external stimuli, such as heat, moisture, or light. This enables the creation of dynamic, self-assembling structures, which are particularly relevant for the development of biomimetic actuators that can adapt to their environment. Gladman et al. [24] applied the principles of four-dimensional printing, combining three-dimensional (3D) printing with responsive materials, to control the printing path and induce anisotropic swelling in nanofiber composite hydrogels, creating biomimetic actuators that exhibit bending, twisting, and other deformations upon exposure to water. Since then, an increasing number of researchers have applied 4D printing technology to the design and fabrication of biomimetic actuators, achieving promising results. For instance, Deng et al. [25] proposed a 4D printing strategy that combines laser direct-write paths with a changing magnetic field to guide the magnetic-driven deformation of composite materials, designing biomimetic actuators that undergo stretching and bending under magnetic control. Zhang et al. [26] developed a 4D printing strategy using UV light curing to embed pre-stretched elastomers, designing cross-shaped grippers with electric-responsive deformation for gripping objects of various shapes. Cecchini et al. [27] used 4D printing to fabricate flexible actuators that mimic the form, driving mechanism, and static performance of Geraniaceae seeds, developing a humidity-responsive biomimetic actuator for environmental soil exploration.
For simple bending and twisting deformations, the theoretical models established by Reyssat et al. [16] and Armon et al. [28] can guide the functional tuning of 4D printed actuators. However, for helical deformations involving large geometric nonlinearities in 3D space, obtaining an analytical solution that links the actuator’s structural parameters to its helical deformation characteristics is challenging [23,29].
Therefore, this study proposes the design of a thin-walled biomimetic actuator with a bilayer asymmetric composite structure, along with the simulation of its water-induced helical deformation process using a numerical model. Subsequently, experimental samples are fabricated using 4D printing technology, combining 3D printed fiber scaffolds with water-absorbing polyurethane rubbers. The experimental results are used to correct the numerical model. Finally, the corrected numerical model is employed to study how the structural parameters of the fiber scaffold affect the helical deformation characteristics of the biomimetic actuator, and its functionality as a gripper for retrieving small target objects from narrow pipes is verified. This research aims to provide a solid foundation for the development of specialized actuators for narrow-space applications.

2. Structural Design and Numerical Simulation of the Biomimetic Actuators

As shown in Figure 1a, the biomimetic actuator consists of a two-layer composite structure, comprising a thermoplastic polyurethane (TPU95A, Esun Industrial Co. Ltd., Shenzhen, China) fiber scaffold and a water-absorbing polyurethane rubber (PJ-400, Ruida Rubber Engineering Limited, Henghui, China). The overall dimensions of the actuator are l × w × h. The superabsorbent elastomer (yellow material in Figure 1) undergoes isotropic volumetric strain upon water absorption, providing the driving force for actuator deformation. The fiber scaffold is composed of supporting fibers (green material in Figure 1) and guiding fibers (red material in Figure 1). The supporting fibers are evenly spaced along the actuator’s axial direction (z-axis in Figure 1). The guiding fibers form an angle θ (fiber angle) with the actuator’s axial direction. Due to the use of 3D printing techniques for fabricating the fiber scaffold, the guiding fibers are fabricated using an overhang slow-down technique, resulting in their width (ka) and spacing (Ia) being larger than those of the supporting fibers (width kp and spacing Ip).
Subsequently, the 3D geometric model shown in Figure 1a was converted to a stereolithography format and imported into the finite element analysis software ABAQUS 2021. Experimental tests revealed that the bonding strength of the cured TPU95A and PJ-400 was approximately 1 MPa, which exceeded that of the base material PJ-400. Therefore, in the interaction module, the relationship between the fiber scaffold and the matrix material was defined as a tie constraint, with surface-to-surface discretization. In the boundary condition module, a central edge line on the surface of the biomimetic actuator was identified and fully constrained. To ensure model convergence, mitigate the hourglass problem, and prevent volumetric locking, eight-node linear hexahedral elements with hybrid linear pressure and incompatible modes (C3D8IH) were selected for meshing. After performing a mesh convergence test and considering both computational efficiency and accuracy, the element size was set to 0.12 mm. The final numerical model of the biomimetic actuator, as shown in Figure 1b, contains approximately 33,000 mesh elements.
In order to assign appropriate material properties to the components, tensile tests were conducted on TPU95A and PJ-400 in accordance with ASTM-D882 standards [30]. The resulting stress–strain curves are shown in Figure 2a. Based on the tensile test results, the Young’s moduli for the fiber scaffold (TPU95A) and the matrix material (PJ-400) were set to 59.45 MPa and 0.61 MPa, respectively. As both TPU95A and PJ-400 exhibit hyperelastic behavior, their Poisson’s ratios were set to 0.495. Since the deformation of the biomimetic actuator arises from the volumetric expansion of the matrix material, its expansion coefficient was set to 1.
Since both water absorption expansion and thermal expansion are essentially isotropic volumetric expansions, an initial temperature field with a value of 0 was assigned to the matrix material in the predefined field module of ABAQUS. To facilitate comparison between the numerical simulation results and experimental data, the water absorption expansion behavior of PJ-400 was tested, and the resulting expansion rate curve is shown in Figure 2b. Five geometric nonlinear analysis steps were defined in the analysis step module, with a minimum time step of 10–12 s. The corresponding expansion magnitudes and water absorption times for each analysis step are shown in Table 1. It should be noted that the expansion magnitude in the temperature field corresponds to the material’s linear thermal expansion coefficient, while the expansion rate curve for the water-absorbent elastomer reflects 3D volumetric expansion. Therefore, the expansion magnitude input in the predefined field was set to one-third of the experimental test results. Due to the relatively slow deformation rate driven by water absorption, the static/implicit solver in ABAQUS was used for the numerical computation of the model.
The numerical simulation results for biomimetic actuators with fiber angles θ of 30°, 40°, 50°, and 60° are shown in Figure 3. Driven by the volumetric expansion of the matrix material, the biomimetic actuators exhibit noticeable helical deformation within 30 s. As the water absorption time increases, both the diameter and pitch of the helix progressively decrease. Additionally, the stress contour plots indicate that the Mises stress is primarily concentrated on the supporting fibers of the fiber scaffold, suggesting their role in supporting the overall structure. The numerical simulation results also reveal that, with boundary conditions and other structural parameters held constant (l = 35 mm, w = 4.8 mm, h = 0.26 mm, ka = 0.5 mm, Ia = 0.6 mm, kp = 0.3 mm, Ip = 0.45 mm), the fiber angle θ significantly influences the helical morphology of the biomimetic actuator. The numerical model was established based on idealized material properties, interaction relations, and boundary conditions. Therefore, experimental validation of the numerical simulations is necessary.

3. Preparation of the Biomimetic Actuators and Experimental Validation

As shown in Figure 4a, the fiber scaffold of the biomimetic actuator was fabricated using a fused deposition modeling (FDM) 3D printer (Creality Ender-3 S1 Pro, Creality, Shenzhen, China). Key printing parameters, such as layer height, line width, and printing temperature, were set to 0.1 mm, 0.28 mm, and 215 °C, respectively. The supporting and guiding fibers within the scaffold were printed at different speeds: 60 mm/min for the supporting fibers and 7.8 mm/min for the guiding fibers. To ensure the scaffold had sufficiently thin walls, the distance between the extruder head and the print bed was maintained between 0.1 mm and 0.15 mm. Additionally, a nominal dimension of h = 0.26 mm was used, and samples with dimensional tolerances exceeding 0.01 mm were excluded. A simple and efficient method was developed to fabricate biomimetic actuators, which are shown in Figure 4b. First, the 3D printed fiber scaffold was left at room temperature for 24 h to fully release residual stresses, without the need for any surface treatment. The fiber scaffold was then placed in a rectangular shallow tray made of polytetrafluoroethylene (PTFE). The uncured polyurethane elastomer (in a gel-like state) was poured onto the fiber scaffold, and the surface was repeatedly rolled with a PTFE roller to ensure full adhesion of the gel-like material to the scaffold and to remove excess material. Finally, the sample was cured for 12 h under conditions of 22 °C and 60% relative humidity, resulting in the biomimetic actuator samples.
The helical deformation process of biomimetic actuator samples with different fiber angles (θ = 30°, θ = 40°, θ = 50°, and θ = 60°) under water stimuli is shown in Figure 5. The experimental results indicate that as the fiber angle θ increases, the helix diameter also increases. However, a comparison between the numerical simulation (Figure 3) and experimental results (Figure 5) reveals significant discrepancies in the morphological characteristics, with a contradictory trend in the change in the helix diameter. Therefore, it is necessary to correct the current numerical model.
The deformation of the biomimetic actuator designed in this study is driven by the water absorption-induced expansion of the matrix material (shown in Figure 4c). The expansion mechanism of water-absorbing polyurethane rubber is as follows: hydrophilic polymer networks within the high-water-absorption resin microparticles attract water through capillary action, forming a gel-like structure. As water is absorbed, the polymer chains separate, resulting in an increase in volume. The collective expansion of the microparticles leads to the overall volumetric expansion of the material. These characteristics cause the mechanical properties of the water-absorbing elastomer to differ from those of dry rubber: first, the isotropic volumetric expansion reduces the relative proportion of lateral deformation; second, the small pores formed within the elastomer upon water absorption provide additional degrees of freedom for deformation under stress; and third, the elastomer becomes softer after water absorption, and this softening effect makes it more prone to volumetric rather than lateral deformation under stress. These three factors collectively contribute to a reduction in the Poisson’s ratio (μ) of the water-absorbing polyurethane rubber. Relevant experimental studies have shown that for many water-swollen polymers, the Poisson’s ratio typically falls within the range of 0.1 to 0.3, depending on factors such as the polymer’s crosslink density and water absorption characteristics [31,32].
Therefore, reducing the Poisson’s ratio of the matrix material in the numerical model would make the simulation results more consistent with the experiment. To verify this hypothesis, the Poisson’s ratios of the matrix material were set to 0.4, 0.3, 0.2, and 0.1, and their effects on the helix diameter in the numerical model are shown in Figure 6a. The results indicate that the helix diameter of the model decreases progressively as the Poisson’s ratio increases. The equivalent strain contour plots (maximum principal strain) of the numerical models with different Poisson’s ratios at the same analysis step (corresponding to an expansion time of 20 s) are shown in Figure 6b. The results show that, within the same value range, the color on the matrix material gradually changes from orange-red to green as the Poisson’s ratio decreases. This indicates a progressive reduction in the maximum principal strain. This phenomenon occurs because, in materials with a low Poisson’s ratio, stress in the principal strain direction is partly transferred to the lateral direction. As a result, stress along the principal strain axis decreases, leading to a reduction in the principal strain. Additionally, materials with a low Poisson’s ratio concentrate more volumetric strain in the water absorption direction. They exhibit smaller lateral deformation, which reduces the overall deformation range of the model. This also explains why the helix diameter of the model decreases as the Poisson’s ratio increases.
Through iterative comparisons with experimental results, the Poisson’s ratio of the matrix material was finalized as 0.18. The simulation results of the four corrected numerical models are shown in Figure 7. At the same time, the corrected models’ simulation results now closely match the experimental observations in terms of helical morphology. Figure 8 compares the helix diameters obtained from the numerical models and experimental measurements. Compared to the uncorrected models (Figure 8a), the corrected models (Figure 8b) exhibit a significantly improved agreement with the experimental data, achieving a similarity of over 90%. Errors may be introduced during the testing of material mechanical properties, printing of the fiber scaffold, fabrication of actuator samples, and data measurements.
To evaluate the repeatability of the experimental results, we calculated the coefficient of variation (CV) for the experimental measurement data, as shown in Figure 8. The calculation results indicate that the coefficients of variation for the experimental samples with fiber angles ranging from 30° to 60° are 5.74%, 3.95%, 7.06%, and 12.9%, respectively. This suggests that the influence of the material properties and manufacturing process conditions on the helical deformation characteristics of the biomimetic actuators is minimal. However, the numerical model is based on idealized material properties, interactions, and boundary conditions. Additionally, issues such as mesh distortion and the hourglass effect in the numerical model can also affect computational accuracy. Nevertheless, the corrected numerical model can still be considered an effective tool for analyzing the deformation mechanisms of the biomimetic actuator and guiding its structural optimization design.

4. Helical Deformation Mechanism Analysis and Structural Optimization

To analyze the mechanical mechanism of helical deformation in the biomimetic actuator, the equivalent strain (maximum principal strain) contour plot shown in Figure 9a was obtained using the corrected numerical model. At the same analysis step (corresponding to an expansion time of 20 s), the principal strain in the numerical models with different fiber angles was almost entirely concentrated in the matrix material of the guide layer, showing similar values. In contrast, the strain in the matrix material of the support layer was much smaller due to the constraints imposed by the surrounding rigid fibers. Figure 9b shows the strain tensor distribution for the four numerical models, where the principal strain tensor is primarily oriented towards the normal of the guiding fibers. Based on the above information, the primary mechanism of helical deformation in the biomimetic actuator is identified: compared to the flexible matrix material, the fiber scaffold structure possesses sufficient stiffness to constrain expansion in a specific direction. The support fibers restrict axial strain in the matrix material, while the guide fibers force the strain to develop along their normal direction. Ultimately, the bilayer structure formed by the support and guide fibers converts the isotropic volumetric expansion induced by water absorption in the matrix material into anisotropic helical deformation. Additionally, varying the fiber angle can alter the morphological characteristics of the helical deformation.
From the perspective of the mechanical properties, the support layer of the actuator is a kind of unidirectional fiber-reinforced composite; thus, its elastic modulus (Ep) satisfies the fiber–matrix rule of mixture:
Ep = Efpvfp + Em(1 − vfp),
where Efp is the Young’s modulus of the reinforced fibers, vfp is their volume fraction, and Em is the Young’s modulus of the matrix. Since the stiffness of the reinforced fiber is much higher than that of the matrix, Equation (1) can be simplified as Ep ≈ Efpvfp. Therefore, in addition to the fiber angle θ, it is also essential to investigate the effect of the support fiber volume fraction (vfp) on the helical deformation characteristics of the biomimetic actuator. The corrected numerical model provides an effective tool; thus, four numerical models with different support fiber volume fractions (vfp) were established. To maintain a constant width, the volume fraction was adjusted by varying the count (n) and spacing (Ip) of the support fibers; the corresponding relationship is shown in Table 2.
The numerical simulation results for the four models are shown in Figure 10; they reveal an increasing trend in the actuator’s helical diameter with the rise in support fiber volume fraction. According to material mechanics theory, when other boundary conditions remain constant, a solid with higher stiffness will experience relatively smaller deformations. The reduction in the overall deformation of the biomimetic actuator leads to an increase in both the helical diameter and pitch, thereby slowing down the helical deformation rate. However, for the biomimetic composite material, a higher fiber density contributes to improved overall strength and load-bearing capacity [33,34].
Based on the trends revealed by the numerical simulations and the functional requirement for gripping and retrieving small targets in narrow pipes, a structural optimization design was carried out for the biomimetic actuator. A fiber angle of 40° was selected for the fiber scaffold within the range of 30° ≤ θ ≤ 60° to achieve a more balanced scale of the actuator’s helical diameter and pitch. A support fiber volume fraction of 54.79% was chosen to enhance the actuator’s structural stiffness, strength, and load-bearing capacity. To enable the actuator to enter narrower spaces, its width was reduced to w = 3.115 mm. Figure 11 shows the helical deformation process of the biomimetic actuator after structural optimization. At the same time, the helical shape features from both the numerical simulation and experimental results are nearly identical, further validating the accuracy of the corrected numerical model. Additionally, the simulation results indicate that after 60 s of contact with water, the helical diameter of the actuator becomes less than 4 mm, allowing it to enter narrow pipes with diameters smaller than 5 mm.

5. Validation of the Object Retrieval Function in Narrow Lumen

In order to test the object retrieval function of the biomimetic actuator in a narrow lumen, the following experiment was designed. As shown in Figure 12, a cylindrical target with a diameter of 3.5 mm was placed inside a glass pipe with an average lumen diameter of 4 mm. In this scenario, conventional tools such as tweezers, clamps, and hooks are ineffective for retrieving the target. Therefore, the optimized biomimetic actuator was soaked in water for 60 s to form a hollow helical tube with a diameter smaller than 4 mm. The helical actuator was then inserted into the pipe using a guidewire and positioned over the target for 60 s. During this time, the actuator radially contracted to securely grasp the target, demonstrating its excellent adaptability. Finally, the actuator, along with the target, was retrieved from the glass pipe by means of the guidewire.
In recent years, various biomimetic actuators inspired by the structures of elephant trunks [35], octopus tentacles [36], human hands [37], etc., have been developed and have garnered widespread attention. While these actuators have significantly simplified their designs, they still require relatively large power sources and include components such as airbags, wires, and skins, which limit their further miniaturization. Moreover, they still rely on significant bending deformations to grasp objects, which results in lower adaptability and an increased risk of object slippage.
In contrast, the biomimetic actuator proposed in this study features a compact structure with an average thickness of only 0.26 mm, addressing the poor performance of traditional actuators in confined spaces. Additionally, unlike the conventional bending deformation model, the helical structure enables the actuator to wrap around an object 360°, offering higher spatial efficiency and enhanced grasping stability. Furthermore, this actuator is simple to manufacture and cost-effective, making it suitable for single-use applications without the need for frequent reuse, thereby avoiding the complexities and costs associated with repeated usage. However, despite these advantages, the biomimetic actuator proposed in this study has some limitations. Its maximum load is only 0.9 g, and its deformation speed is relatively slow, restricting its application in scenarios that require higher loads, faster deformation rates, or larger operational spaces.

6. Conclusions

In this study, a biomimetic actuator with a bilayer asymmetric composite structure was designed, and a corresponding numerical model was developed. The numerical simulation results indicate that the actuator undergoes helical deformation driven by the water absorption of the matrix material. A thin-walled biomimetic actuator sample, with a thickness of only 0.26 mm, was fabricated using 4D printing technology. The numerical model was corrected through experiments, leading to the conclusion that the Poisson’s ratio of the water-absorbing polyurethane rubber is significantly lower than that of typical hyperelastic rubbers. Using the corrected model, the helical deformation mechanism of the actuator was revealed, and the influence of the structural parameters of the fiber scaffold on the helical shape was analyzed. The helical diameter of the actuator increases with the fiber angle θ, while the pitch decreases accordingly. Increasing the fiber volume fraction enlarges the helical diameter and improves structural stiffness. The experiment demonstrated that the structurally optimized biomimetic actuator is capable of gripping and retrieving small targets from narrow pipes with a diameter of less than 5 mm. Moreover, as the helical deformation continues, the actuator automatically tightens around the target, showcasing its excellent adaptability. The findings provide a solid theoretical and technical foundation for the development of novel flexible grippers designed for narrow spaces with superior adaptability. Specifically, the numerical modeling method can be applied to simulate the deformation process of the actuator based on the selected materials. The simulation results can then be used to inform the structural optimization design of the actuator, ensuring that it meets the requirements for operation in narrow pipes of specific dimensions. Finally, specialized grippers can be fabricated using 4D printing technology. The proposed biomimetic actuator’s unique design offers enhanced adaptability, high spatial efficiency, and stability, making it ideal for applications in soft robotics, minimally invasive medical devices, and other flexible actuator systems. Future research will focus on scaling the actuator for more complex systems, increasing its load capacity and deformation speed, and exploring alternative materials and actuation mechanisms to further enhance its versatility across a wider range of applications.

Author Contributions

Conceptualization, C.Z. and J.Z.; methodology, C.Z. and L.D.; software, C.Z.; validation, J.Z., H.H., and L.D.; formal analysis, H.H.; investigation, L.D.; resources, C.Z.; data curation, H.H.; writing—original draft preparation, C.Z.; writing—review and editing, J.Z. and L.D.; visualization, H.H.; supervision, J.Z.; project administration, J.Z.; funding acquisition, J.Z. All authors have read and agreed to the published version of the manuscript.

Funding

This research was supported by the National Natural Science Foundation of China (Grants No. 52475292 and 52105295), the Natural Science Foundation of the Jiangsu Higher Education Institutions of China (Grant No. 24KJA460001), Changzhou Science and Technology Project (Grants No. CJ20230040 and CJ20230038).

Data Availability Statement

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Conflicts of Interest

The authors declare no conflicts of interest.

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Figure 1. The geometrical structure (a) and finite element model (b) of the biomimetic actuators.
Figure 1. The geometrical structure (a) and finite element model (b) of the biomimetic actuators.
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Figure 2. Evaluation of the material properties constituting the biomimetic actuator. (a) Representative stress–strain curves for TPU95A and PJ-400. (b) The swelling ratio vs. time curve for the water-absorbing polyurethane rubber specimens.
Figure 2. Evaluation of the material properties constituting the biomimetic actuator. (a) Representative stress–strain curves for TPU95A and PJ-400. (b) The swelling ratio vs. time curve for the water-absorbing polyurethane rubber specimens.
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Figure 3. Simulation results of numerical models with fiber angles θ of 30°, 40°, 50°, and 60°.
Figure 3. Simulation results of numerical models with fiber angles θ of 30°, 40°, 50°, and 60°.
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Figure 4. Four-dimensional printing process of the biomimetic actuators. (a) Three-dimensional printing of the fiber scaffold. (b) Assembly of the water-absorbing polyurethane rubber with the fiber scaffold. (c) Helical deformation behavior driven by water absorption-induced expansion of the matrix material.
Figure 4. Four-dimensional printing process of the biomimetic actuators. (a) Three-dimensional printing of the fiber scaffold. (b) Assembly of the water-absorbing polyurethane rubber with the fiber scaffold. (c) Helical deformation behavior driven by water absorption-induced expansion of the matrix material.
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Figure 5. Helical deformation process of the biomimetic actuator samples with fiber angles θ of 30°, 40°, 50°, and 60°.
Figure 5. Helical deformation process of the biomimetic actuator samples with fiber angles θ of 30°, 40°, 50°, and 60°.
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Figure 6. Effect of the Poisson’s ratio μ of the matrix material on the numerical models. (a) Variation in the helix diameter with different Poisson’s ratios of the matrix material. (b) Effect of the Poisson’s ratio of the matrix material on the equivalent strain distribution of the numerical model.
Figure 6. Effect of the Poisson’s ratio μ of the matrix material on the numerical models. (a) Variation in the helix diameter with different Poisson’s ratios of the matrix material. (b) Effect of the Poisson’s ratio of the matrix material on the equivalent strain distribution of the numerical model.
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Figure 7. Simulation results of the corrected models with different fiber angles.
Figure 7. Simulation results of the corrected models with different fiber angles.
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Figure 8. Comparison of helical diameter between experimental measurements and numerical simulations of biomimetic actuators. (a) Comparison of experimental measurements and simulated results from the uncorrected numerical models. (b) Comparison of experimental measurements and simulated results from the corrected numerical models.
Figure 8. Comparison of helical diameter between experimental measurements and numerical simulations of biomimetic actuators. (a) Comparison of experimental measurements and simulated results from the uncorrected numerical models. (b) Comparison of experimental measurements and simulated results from the corrected numerical models.
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Figure 9. Helical deformation mechanism analysis of the biomimetic actuator. (a) Equivalent strain distribution of the numerical models with different fiber angles. (b) Equivalent strain tensor contour plot of the numerical models with different fiber angles.
Figure 9. Helical deformation mechanism analysis of the biomimetic actuator. (a) Equivalent strain distribution of the numerical models with different fiber angles. (b) Equivalent strain tensor contour plot of the numerical models with different fiber angles.
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Figure 10. Numerical simulation results for the corrected models with different support fiber volume fractions.
Figure 10. Numerical simulation results for the corrected models with different support fiber volume fractions.
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Figure 11. Comparison of the numerical simulation and experimental results of the helical deformation process of the optimized biomimetic actuator.
Figure 11. Comparison of the numerical simulation and experimental results of the helical deformation process of the optimized biomimetic actuator.
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Figure 12. Experimental process of gripping and retrieving a cylindrical target in narrow lumen using the biomimetic actuator.
Figure 12. Experimental process of gripping and retrieving a cylindrical target in narrow lumen using the biomimetic actuator.
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Table 1. Relationship between expansion amplitude and water absorption time in the predefined field.
Table 1. Relationship between expansion amplitude and water absorption time in the predefined field.
Analysis StepExpansion Magnitude (%)Water Absorption Time (s)
Step 19.3710
Step 212.6215
Step 316.1120
Step 419.4825
Step 522.2230
Table 2. Relationship between fiber count, spacing, and volume fraction.
Table 2. Relationship between fiber count, spacing, and volume fraction.
Model IDFiber CountFiber Spacing (mm)Volume Fraction (%)
150.82529.01
260.60035.45
380.34348.35
490.26354.79
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MDPI and ACS Style

Zhao, C.; Duan, L.; Hua, H.; Zhang, J. Exploring Water-Induced Helical Deformation Mechanism of 4D Printed Biomimetic Actuator for Narrow Lumen. Machines 2025, 13, 31. https://doi.org/10.3390/machines13010031

AMA Style

Zhao C, Duan L, Hua H, Zhang J. Exploring Water-Induced Helical Deformation Mechanism of 4D Printed Biomimetic Actuator for Narrow Lumen. Machines. 2025; 13(1):31. https://doi.org/10.3390/machines13010031

Chicago/Turabian Style

Zhao, Che, Lei Duan, Hongliang Hua, and Jifeng Zhang. 2025. "Exploring Water-Induced Helical Deformation Mechanism of 4D Printed Biomimetic Actuator for Narrow Lumen" Machines 13, no. 1: 31. https://doi.org/10.3390/machines13010031

APA Style

Zhao, C., Duan, L., Hua, H., & Zhang, J. (2025). Exploring Water-Induced Helical Deformation Mechanism of 4D Printed Biomimetic Actuator for Narrow Lumen. Machines, 13(1), 31. https://doi.org/10.3390/machines13010031

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