Fiber-dominated Soft Actuators Inspired by Plant Cell Walls and Skeletal Muscles

Morphing botanical tissues and animal muscles are all fiber-mediated composites, in which fibers play a passive and active role, respectively. Herein, inspired by the mechanism of fibers functioning in morphing botanical tissues and animal muscles, we propose two sorts of fiber-dominated composite actuators. First, inspired by the deformation of awned seeds in response to humidity change, we fabricate passive fiber-dominated actuators using non-active aligned carbon fibers via 4D printing method. The effects of process parameters, structural parameters, and fiber angles on the deformation of the printed actuators are examined. The experimental results show that the orientation degree is enhanced, resulting in a better swelling effect as the printing speed increases. Then, motivated by the actuation mechanism of skeletal muscle, we prepare active fiber-dominated actuators using active polyurethane fibers via 4D printing and pre-stretching method. The effect of fiber angle and loading on the actuation mode is experimentally analyzed. The experimental results show that the rotation angle of the actuator gradually decreases with the angle from 45° to 60°. When the fiber angle is 0° and 90°, the driver basically stops rotating while shrinking along the loading direction. Based on the above actuation mechanisms, identical contraction behaviors are realized both in passive and active fiber-dominated soft actuators. This work provides a validation method for biologically actuation mechanisms via 4D printing technique and smart materials and adds further insights to the design of bioinspired soft actuators.


Introduction
For survival and reproduction, plants and animals have evolved a diverse of delicate fiber-dominated structural materials to adapted to dynamic environment [1][2][3]. In plant system, non-active cellulose fibers are utilized to direct the homogeneous cytoplasmic matrix with oriented shape morphing features [4][5][6]. A well-known example is the automatic deformations of pine cone scales [7], whose symmetrically arranged cellulose fibers enable folding in wet and opening in dry conditions for efficient spreading seeds. In animal skeletal muscles [8][9][10], the internal constraints of aligned active muscle fibers is capable of modulating the mechanical performance by increasing its range of operating velocities.
Although fibers permit the movement of both animal muscles and plant tissue, the roles played by the fibers are quite different. Lacking muscles [11], plants use a variety of energy sources and release mechanisms to produce deformation and movements (pine cones [12][13][14][15], awned seeds of family Geraniaceae [7,16] and pea pods [17,18]). Most of plant pericarp cell walls are composed of reinforcing fibers (non-stretchable cellulose fibers [19][20][21]) embedded in matrix materials [5] (water-swelling matrixes containing hemicelluloses and lignin hemicelluloses and lignin) that are known as natural fiber-reinforced composites [22][23][24]. As a result, the architectures of stiff cellulose fibrils embedded in a swelling hygroscopic matrix limit the isotropic expansion/contraction of the matrix material under humidity stimulation. It indicates a general principle that the swelling behaviors can be controlled by structured fibers.
In contrast to the role of fiber played in plant system, the mechanical output of muscles is more strongly affected by the length changes and shortening velocity of muscle fibers [25,26]. The muscle fiber is comprised of a number of myofibrils arranged in parallel and comprised of sarcomeres arranged in-series, which usually exhibit an angle to connective tissue's line and thus determines the muscle's mechanical function [8]. Hill proposed a theoretical model for the force-velocity relationship during muscle movement, in which muscle output force decreases significantly with increasing muscle fiber contraction velocity, favoring the output of muscle velocity at low loads and force output at high loads [9,[27][28][29][30]. The active actuation mechanisms of muscles relying on regional variation in architectures provide a feasible way for tuning the mechanical and deformation behaviors.
With the rapid development of 4D printing and smart materials [31][32][33][34][35][36][37], the principles of passive actuation in plants as well as active actuation in animals have been intensively studied. However, the mechanisms underneath are still unexplored and have not been verified by elaborated experiments. In fiber-reinforced composites, the deformable matrix leads the non-deformable restricted fibers to produce complex deformation under external stimulation, which is called passive driving. In fiber-reinforced composites, the deformable fibers drive the non-deformable matrix to produce nonuniform deformation under external stimulation, which is called active drive. Here, 4D printing-based approaches is adopted to allow a deeper insight into the mechanism of active/passive fiber-dominated actuators. Inspired by awned seeds of family Geraniaceae, passive carbon fiber-reinforced polyurethane composites are chosen to produce spiral, twisting and coiling motions under diurnal humidity, as shown in Fig. 1a. Inspired by the hierarchical and anisotropy structure of skeletal muscles, active polyurethane fiber-reinforced silicone composites are selected to investigate the dynamic mechanical feedback with fiber orientations, as presented in Fig. 1b. The study provides proofs for the mechanism underneath the deformations and mechanical outputs of biological fiber-dominated composites, and builds a solid theoretical basis for the further exploration of soft robotic.

Preparation of Fiber-dominated Soft Actuator
In plants, the deformable matrix and confined fibers generate delicate deformations. We prepared a passive fiber-dominated soft actuator consisting of the stimulus-responsive polyurethane (Hengchuang Construction Engineering Material Co., Ltd., China) matrix and non-responsive carbon fibers (Hangzhou Gaoke Composite Material Co., Ltd., China). First, the carbon fibers of 1, 3 and 5wt.% were added to the polyurethane, respectively. The composite slurry is placed in the high speed disperser (Ningbo Scientz Biotechnology Co., Ltd., China) and stirred thoroughly for 2 min at the speed of 2800 r/min to avoid fiber agglomeration. Second, the prepared composites were printed into the target shape using the DIW method. Finally, the printed prototypes were Fig. 1 The schematic diagram of the fiber-dominated prototypes. a The passive fiber-dominated microstructure of the geranium family in plant system. b The active fiber-dominated microstructure of skeletal muscle in animal system 1 3 cured at room temperature for 5 h. The rheological properties of the composites are critical to the printing process and rheological properties are tested ( Figure S1).
In animals, active deformation of muscle fibers drives the movement of connective tissue. Mimicking this mechanism, we prepared active fiber-dominated soft actuators consisting of shape memory polyurethane (Kyoraku Co., Ltd., Japan) fiber and silicone matrix (Ecoflex 00-50). The fabrication formulation is shown in Figure S2. The polyurethane thin film is printed using the FDM printing process. Then, the thin film is pre-stretched in the thermostat chamber (Shanghai Siwei Instrument Manufacturing Co., Ltd., China) to double the length at 60℃. This is due to the fact that the glass transition temperature of shape memory polyurethane is 45℃. The films are cut to different angles to form the target shapes. Then, the film is placed in the mold and embedded into the silicone matrix. Finally, rest at room temperature for 12 h to cure the composite.

Characterization
To evaluate the orientation of the fibers in the composites in the passive fiber-dominated soft actuator, an integrated microscope (Stereo Discovery V20, Zeiss) was used for observation. The approximate angle of fiber orientation of ± 15° is defined as an index to assess the effect of fiber alignment. Image J was used to count the degree of fiber orientation. In the passive fiber drive, it was placed in water at 25 °C and observed the way of deformation. In the active fiber-dominated actuator, they are placed in the thermostat chamber at 60 °C for actuation experiments. When the temperature is higher than the glass transition temperature of the active fibers (shape memory polyurethane), the muscle fibers actively shrink, and drives the motion of the actuators. We prepared active fiber-driven actuators with different fiber angles so that we could observe the effect of fiber angle on the movement pattern of the actuators.

Passive Fiber-dominated Soft Actuator Inspired by Plants
By mimicking the shape morphing behaviors caused by swellable cytoplasmic matrix and confining cellulose fibers in plants, we developed passive fiber-dominated soft actuators which consists of the stimulus-responsive polyurethane matrix and non-responsive carbon fibers. The fiber length distribution is shown in Figure S2, which ranges to 100-200 µm. We tested the effect of process parameters on the swelling properties of carbon fiber-reinforced polyurethane composites with fiber content of 3wt.%, as shown in Fig. 2. During the printing process, the fiber-doped slurry is extruded from the nozzle under air pressure and deposited on the substrate (Fig. 2a). The shearing force in the extrusion nozzle and the friction between the slurry and the platform enable the fiber oriented in the deposition direction and the degree of fiber alignment determined by the printing parameters. Since the deformation patterns are closely associated with the fiber alignment, it allows us to program the degree of deformation through the printing parameters.
We investigated the effect of printing speed, nozzle diameter and fiber content on the fiber orientation. The approximate angle of fiber orientation of ± 15° was calculated as an indicator to evaluate the effect of fiber alignment, as shown in the inset of Fig. 2b. The experimental results show that the fiber orientation effect gradually increases as the printing speed increases from 5 to 25 mm/s. In addition, the filament exhibits smaller diameters as the printing speed increases, as shown in Fig. 2c. As the printing speed gets higher, higher uniaxial drag speed drives the elongated and thinner filaments in the print direction. As the filament diameter gradually decreases, the fibers are subjected to a greater shearing and friction force on the outer wall of the filament. As a result, increasing printing speed leads to higher degrees of fiber orientation. It should be noted that, the extruded filament diameter is relatively small at the nozzle diameter of 0.34 mm, which prevents the extruded filament from being fully deposited onto the printing platform as the printing speed increases. Therefore, the effects of fiber orientation and extruded filament width were measured only at printing speeds of 5 and 10 mm/s when the nozzle diameter was 0.34 mm. The nozzle diameter has a significant effect on the degree of fiber orientation. As the nozzle diameter increases from 0.34 to 0.61 mm, the extent of fiber orientation gradually decreases. With the increase of nozzle diameter, the extruded filament diameter becomes larger. The material in the nozzle undergoes the same pressure during the printing process. Accordingly, with the rise of nozzle diameter, the shearing force on the fibers get reduced and leads to the lower orientation degrees.
To investigate the swelling properties of the fiber-reinforced composites, the specimens were immersed in water for 12 h after curing. The swelling rate of the composites was calculated by measuring the axial length and radial width after swelling. The calculations were performed as shown in Eq. 1 and Eq. 2.
where α ∥ is the axial expansion rate, m 1 is the axial length before expansion, and m 2 is the axial length after expansion.
where α ⊥ is the radial expansion rate, n 1 is the radial width before expansion, and n 2 is the radial width after expansion.
The relationship between the axial swelling rate, radial swelling rate and the printing process parameters is shown in Fig. 2e. The results show that the process parameters have a significant effect on both axial and radial expansion rates. The radial expansion rate gradually increases with the rising of printing speed. As shown in previous results, the degree of fiber orientation gradually increases with rising printing speed, resulting in an enhanced tendency of fiber orientation along the axial direction. Consequently, during the expansion process, the effect of fiber limiting the expansion of the composite along the axial direction is enhanced, and the limiting expansion effect along the radial direction is weakened. In the experiment, the effect of the process parameters on the axial expansion rate and radial expansion rate is inconsistent, and the expansion rate anisotropy coefficient α is defined as follows.
where, α ⊥ represents the width expansion rate, α ∥ represents the length expansion rate.
The effect of process parameters on the anisotropy coefficient of swelling rate was investigate (Fig. 2f). The anisotropy coefficient of expansion gradually increases with the growing printing speed. Meanwhile, as the nozzle diameter increases, the fiber orientation effect gradually decreases, leading to a decrease in the expansion rate. By investigating the effect of process parameters on the fiber orientation and expansion rate, the optimal process parameters were determined. The printing speed of 10 mm/s, the fiber content of 3 wt.%, the air pressure of 1 MPa and the nozzle diameter of 0.52 mm were chosen for further experiment. We also tested the effect of process parameters on the swelling properties of carbon fiber-reinforced polyurethane composites with fiber content of 1 and 5 wt.%, as shown in Figure S4, S5.
The experiments show that the printing process parameters are strongly related to the degree of fiber orientation and the swelling properties. During the extrusion process, the fibers are mainly subjected to shear forces exerted by the nozzle. The higher the shear to which the fibers are subjected, the higher the alignment along the axial direction of the nozzle and thus along the axial direction of the composite filament (printing direction). When the fibers are deposited onto the substrate, the fibers are mainly subjected to dragging forces during the advancing of the nozzle as well as to the frictional forces of the substrate. The greater the drag force, the greater the squeezing force on the fibers, which causes the fibers to align in the direction of the drag force. As the print speed gradually increases, the drag force between the nozzle and the substrate increases, resulting in an increase in the alignment of the fibers in the direction of the print. As the nozzle diameter decreases, the shear force exerted by the nozzle on the composite increases, causing the fibers to align in the printing direction. The fibers act as a rigid part to limit the expansion of the polyurethane material when stimulated by humidity. The direction of fiber alignment will, therefore, limit the expansion of the polyurethane in the direction, resulting in a greater expansion of the polyurethane in the other direction than in the direction of fiber alignment. In summary, it can be concluded that the process parameters influence the degree of fiber orientation, which further influences the swelling properties of the composite, which corresponds to the experimental results.
To investigate the effect of fiber orientation on the deformation mod, we prepared carbo fiber-reinforced polyurethane composites with bilayer structures in which the fibers have different orientation angles. The orientation angles of the bilayer structure were 0°/90°, 15°/75°, 30°/60° and 45°/45°, respectively. The printed specimens were 80*10*1 mm in size, cured at room temperature for 72 h, and subsequently placed in water for 12 h to allow sufficient expansion. The orientation of the fibers resulted in anisotropic swelling of the composite. Depending on the alignment angle in the fiber-reinforced polyurethane composite, the specimens have different bending curvatures and pitches after deformation.
The bending deformation of the bilayer structure is mainly due to the anisotropic expansion of the bilayer structure under external stimulation, resulting in the mismatch of stresses in the bilayer structure. Under the humidity stimulation, the first layer is deformed mainly in the radial direction, and the second layer is deformed mainly in the axial direction. The deformation of one layer in the radial/axial direction will be suppressed by the other layer. By controlling the printing path of the upper and lower layers of the bilayer structure, the way of deformation of the specimen can be controlled to produce bending or twisting deformation. The results are shown in Fig. 3a, b. When the orientation angle of the double-layer structure changes from 0°/90° to 45°/45°, the deformation changes from bending to curling. The bending curvature gradually becomes larger, while the pitch gets smaller. When the double-layer structure is 0°/90°, the double-layer structure curls into a circle and the bending curvature of the composite double-layer structure is 0.2 mm minimum, as shown in Fig. 3c. When the orientation angle of the bilayer structure changes from 15°/75° to 45°/45°, the deformation mode changes to spiral deformation. When the orientation angle changes from 15°/75° to 45°/45°, the curvature of the bilayer structure gradually increases and the pitch gradually decreases. In addition, the deformation of the double-layer structure can be regulated by programming the printing parameters. The two representative deformations, 0°/90° and 45°/45°, were chosen to investigate the effect of printing width on deformation. When the double-layer structure is 0°/90°, as shown in Fig. 3d, the curvature of the double-layer structure decreases from approximately 0.9 to 0.4 mm as the printing width increases from 2 to 10 mm. As shown in Fig. 3e, g, when the double-layer structure is 45°/− 45°, the pitch increases and the curvature decreases as the width increases from 2 to 10 mm.
We prepared the bilayer structure by printing the slurry on paper substrates. The dimensions of the style are 80 × 10 × 0.5 mm, as shown in Fig. 4a. In the two-layer structure, the composite material acts as the active layer and the paper as the passive layer. The fiber orientations in the active layer are 0°, 15°, 30°, 45°, 60°, 75° and 90°. Under humidity stimulation, the active layer produces anisotropic expansion while the passive layer produces isotropic expansion, resulting in a bilayer structure deformation dependent on the fiber angle (Moive1). The stress mismatch between the bilayer structures leads to curling and helical deformation of the composites, as shown in Fig. 4b-h. In addition, we mimicked the snowflake structures to generate snowflakelike deformations by programming the fiber orientations in Fig. 4i.

Active Fiber-dominated Soft Actuator Inspired by Animal Muscles
By mimicking the dynamic mechanical output caused by regional heterogeneity in muscle fiber of animals, we developed active fiber-dominated soft actuators that consists of shape memory polyurethane fiber and silicone matrix. We prepared four different active fiber-dominated actuators with the angle between the fiber and the matrix of 0°, 45°, 60° and 90°, respectively (Fig. 5a, d, g, j).
To characterize the mechanical properties of the active fiber-dominated actuator, the contraction experiments by applying weights of 10, 20 and 30 g to the four actuators were conducted. Figure 5b, e, h, k shows four types of active fiber-dominated actuators oriented at 0°, 45°, 60° and 90° and loaded with 10 g weights. Figure 5c, f, i, l shows the state of the four active fiber-dominated actuators after contraction.
Similar to muscle fibers, the active fiber-dominated actuators are also aligned at certain angle to the action direction. In Fig. 5m, the muscle thickness of the actuator shows a significantly decreasing trend with the increase of the load, which benefits fiber rotation at low loads and resists fiber rotation at high loads. In Fig. 5n, the degree of fiber rotation declined systematically with increasing levels of force. Fig. 4 The composite/paper passive fiber actuator. a The schematic diagram of the actuator for the carbon fiber-reinforced polyurethane composite/ paper. The schematic diagram, the physical diagram, and the physical diagram after deformation of the bilayer structure for different fiber angles: 0° b, 15° c, 30° d, 45° e, 60° f, 75° g, and 90° h. i The schematic diagram, physical diagram and picture after deformation of the snowflake structure The rotation angle of fiber decrease as the angle from 45° to 60°. When the angle is 0° to 90°, the rotation angle of fiber was essentially zero and contracted along the direction of the loading. The ratio of muscle fiber velocity to whole muscle velocity is referred to as the architectural gear ratio (AGR) of the muscle [28,[38][39][40]. Muscle gearing adheres to the principle that velocity advantages come at the cost of a reduction in force. In Fig. 5o, the AGR decreases significantly as the load increases. In addition, the AGR of the actuator decreases gradually with the angle from 0° to 90°.
To verify the results concluded from the active fiber-dominated actuator, we performed simulations using the finite element analysis software (Abaqus CAE). We built a finite element method using ABAQUS software to study the deformation response of an active fiber-dominated soft actuator under external loads. To simulate the response of the actuator to temperature changes, we modeled the shrinkage cell as a solid body. The symmetry layer is used to model the mesh around the contraction cell, and the flexible layer is modeled as an elastic material. The interaction between the contraction cell and the s flexible layer is set as a tie constraint. The upper end of the actuator is fixed and different loads are applied to the lower end to mimic the boundary conditions and loaded weights in the experiment. The simulation outputs the thickness, width, angular variation as well as the stresses and strains of the actuator, as shown in Fig. 6. The effects of loads and fiber-to-muscle angles on the mechanical performance were verified. Muscle thickness, the angles of fiber rotation and AGR were measured and compared using experiments and simulations, respectively. As shown in Fig. 6a, b, the simulation model and experimental models were displayed with different loads and angles between fiber and muscle before loading test. Figure 6c, d shows the simulation results and experimental results of the models with different loads and fiber-to-muscle angles after loading tests. We also compared the experimental and simulated results for the active fiber-dominated actuator (Fig. 6e, f, g). As shown in most of the comparisons, the simulations accurately predicted the muscle thickness, rotation angle of fiber and AGR with negligible error and were consistently matching with the experimental date at different loads (Moive2).

Metastructure Design Inspired by Active and Passive Fiber-dominated Structures
Metastructure are rationally designed structured materials whose macroscopic properties are mainly determined by their structures rather than composition. Inspired by the passive actuation mechanism of plant tissues and the active actuation mechanism of animal tissues, buckling structures with active and passive fiber-dominated designs were prepared. The size of the metastructures is 80*10*2 mm. Figure 7a is the schematic diagram of the passive fiberdominated buckling unit, where the carbon fiber-reinforced polyurethane composite material was printed onto paper. Under the stimulation of humidity, the passive fiber-dominated units of metastructure were both buckled to the paper side resulting in an elliptical state as shown in Fig. 7b. Figure 7c shows the schematic diagram of the active fiber-dominated buckling unit, where the pre-stretched polyurethane  Fig. 7d. The approach with passive fiber-dominated and active fiberdominated mechanisms both show great potential for metastructure design and fabrication, and will be promising in the future development of soft robotics.

Conclusion
Fibers serve as a key determinant in the construction of biological materials. Uncovering the mechanism of fibers in dynamic biological materials is critical in promoting the development of high-performance bioinspired actuators.
Based on the mechanism of the active matrix embeds stiffening fibers to achieve different forms of swelling behavior, we fabricated passive fiber-dominated actuators using carbon fiber-reinforced polyurethane composites via 4D printing method. The effects of process parameters and fiber angles on the deformation of the printed actuators were examined. The experimental results show that the process parameters affect the degree of fiber orientation and influence the swelling properties of the composite. Based on the mechanism that passive matrix embedded in flexible fibers can mediate into deformation behavior, we prepared active fiber-dominated actuators using pre-stretched polyurethane fibers reinforced silicone via 4D printing method. The effect of fiber angles and loading on the actuation mode was experimentally analyzed. The experimental results show that the thickness of the actuator becomes progressively thinner as the load gradually increases. Finally, we prepared the same Data Availability Data sharing not applicable to this article as no datasets were generated or analysed during the current study.

Conflict of Interest
The authors declared that they have no conflicts of interest to this work. We declare that we do not have any commercial or associative interest that represents a conflict of interest in connection with the work submitted.
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