Reducing penetration resistance through bio-inspired head oscillation

Animals such as worm lizards can effectively bury themselves in the ground for survival. The burial behavior is realized due to the head oscillation of the reptiles using different strategies. It is hypothesized that the periodic penetration process generated from the anterior part of the animal reduces penetration resistance because it breaks the local force chains in the soil. In this paper, the three-dimensional discrete element method (DEM) modeling method was used to validate this hypothesis to investigate the interaction between a penetrator and the granular material at different scales. The penetrator was simplified as a three-body structure: an oscillating cone, a joint, and a cylindrical body. It was then penetrated through the soil sample vertically with different oscillation velocities. The results show that the oscillation movement can significantly reduce the penetration resistance force. Furthermore, the force chain network of the soil sample was investigated, and comparisons were made among cases, which shed light on the fundamental mechanism of the reduction effect.


Introduction
In nature, a myriad of biological organisms have facilitated the evolution of sophisticated mobility strategies to interact adeptly with granular environments like soils and rocks, thereby executing essential functions including movement, growth, anchorage, and nutrient absorption [1].These organisms dynamically alter their body configurations to diminish penetration resistance, amplify thrust and anchorage, or achieve a conducive amalgam of both [2], [3].
Amphisbaenia, which is commonly referred to as amphisbaenians or worm lizards, encompasses a group of legless squamates, comprising diverse species.Characterized by their elongated bodies, Amphisbaenia possess a body structure that is arranged in annular segments, which are constituted by scales (Figure 1).Previous studies have demonstrated that the burrowing mechanisms of Amphisbaenia may be categorized into three types.(1) oscillatory: worm lizards engage in tunneling by rotating their heads around an axis traversing vertically through the region of their cervical vertebrae whilst simultaneously oscillating their heads along the longitudinal axis of their trunk.(2) shovel snouted: it is observed in species that possess a horizontal, shovel-shaped snout that the elevation of the head results in the compaction of the soil mass above it into the roof, simultaneously expanding the tunnel.(3) keel snouted: it is employed by species featuring a vertical, keel-shaped snout.The alternating rotations of the head to the left and right facilitate soil compaction on either side.Additionally, some worm lizards adopt a combination of the aforementioned three methods [4]- [7].Despite the variations among these 1337 (2024) 012040 IOP Publishing doi:10.1088/1755-1315/1337/1/012040 2 oscillatory patterns, a commonality exists, which is the lateral oscillation along the direction of advancement.Although various researchers have investigated the burrowing performance of worm lizards, a majority of the studies was related to the geometry effect of the skull shapes [8]- [10].
Only a few studies have investigated the impact of biological oscillatory locomotion on soil interaction and penetration resistance.Recent research has shown that at high amplitudes, head movement can decrease penetration force.Newell used a robophysical model to experimentally investigate the impact of oscillatory movement of Amphisbaenia while penetrating horizontally in wet granular media [12].However, the experiment only employed an approximate 17.4-degree oscillation amplitude, and the results exhibited no statistical significance.Another observation emerges from a comparison of burrowing in wet and dry granular media, which indicated that animals burrowing in wet granular media may specifically have to overcome resistance that is approximately four times greater than that of dry granular media [13].However, the authors primarily focused on small-scale experiments to validate the reduction in drilling resistance.There are limited fundamental explanations for this phenomenon.Additionally, comprehensive studies that examine this effect are scarce.The oscillatory penetration process fundamentally constitutes a soil-structure interaction issue.It is advantageous to possess an in-depth comprehension of the soil-structure interaction mechanism across multi-scales given that it may facilitate the translation of the bioinspired oscillatory penetration mechanism into geotechnical terminologies and applications.
The research described in this paper utilized the discrete element method (DEM) to model the dynamic interaction between an oscillatory penetrator and the surrounding granular materials.The parameters of the DEM model were first calibrated and validated using existing laboratory drained triaxial testing data of Ottawa sand F65.The impact of oscillation on the penetration resistance was explored by varying oscillation rates during the penetration of a rod with a joint and a conical tip.

Model construction
The DEM modeling approach has been widely employed to investigate the interactions between soil and structures within the engineering domain [14].This method is not only widely employed in traditional geotechnical engineering, exemplified by cone penetration test [15], pressuremeter test [16], but is equally applicable in biomimetic geotechnical engineering, such as sand-swimming behavior of the sandfish lizard [17], the dynamic penetration behavior of a razor-clam inspired penetrator [18] and rotation on seed's self-burial process [19].Moreover, to balance the computational load and the accuracy of the simulation results, measures such as scaling up the particle size and simplifying the constitutive laws must be implemented.
In this study, the open-source software YADE (Šmilauer 2015) is utilized for executing the DEM simulation tasks.To augment computational efficiency, granular particles are modeled as spherical rigid bodies, and a built-in linear constitutive law is employed to characterize the interaction between any two contacting particles.Fundamentally, the motion of the particles adheres to Newton's second law of motion.The moment transfer law (MTL) is implemented to depict the surface roughness and irregularity of the sand particles [20].
The particle size distribution in this study is based on that of the Ottawa F65 but scaled up by a factor fo 25.Tang conducted the numerical calibration and validation of Ottawa sand F65 [21].Although the micro-parameters are referenced from his settings, the number of particles has been increased, as summarized in Table 1.The sample is produced in a frictionless cylindrical calibration chamber using the "pluviation" technique.Initially, it has a high interparticle friction angle of 45°.To attain the desired porosity, this friction angle is gently decreased.After the unbalanced force drops to 0.001 N, which indicates that the sample is in the quasi-static state, the friction angle is recalibrated.Excess particles are then taken off the top to level the surface.Lastly, the samples undergo a rerun process to reach their ultimate equilibrium state.

Penetrator design scheme selection
Inspired by the head oscillation of Amphisbaenia, the penetrator is designed using two approaches.The first design consists of a cylinder shaft, an expanded joint, and a cone.The cone can slide laterally back and forth along the surface of the expanded joint, with a maximum angle of 90 degrees at each side.The cylinder possesses a length and diameter of 0.15 m and 0.025 m, respectively, which equals the diameter of the cone, and the apex angle of the cone is 60°.The second design comprises a cylinder shaft, an inscribed joint, and a reduced-diameter cone.The cone can swing in the left and right directions along the inscribed joint by 30 degrees.The cylinder possesses a length and diameter of 0.15 m and 0.025 m, respectively, which is times the diameter of the cone.The penetrator is initially positioned such that its tip is located at a distance of 0.01 m above the top surface of the sample.In the DEM simulation of rotary-installed piles [22] and seed awn-inspired rotation [19], it has been observed that the reduction in penetration resistance is not solely associated with the absolute rotational velocity, but rather with the relative slip velocity ( u =     ⁄ ).Although the oscillation direction in this paper is perpendicular to the forward direction rather than along this direction, this parameter setting method can still be referenced.In this study, the vertical penetration speed (  ) for the shaft, joint, and cone was set as 0.04 m/s.The relative slip velocities of u = 0, 1, 4 are utilized to conduct simulations to investigate the impact of head oscillation on penetration resistance force.
To observe the impact of the external dimensional design of the aforementioned two penetrators on penetration resistance, a comparison was made on the magnitude of tip resistance under the conditions of u = 0, 1, and 4.

Reduction of the oscillatory penetration resistance force
Figure 4 shows a comparison of the penetration resistance force and shaft friction force at u = 0, 1, and 4, respectively.The comparison of tip resistances for the two designs when no biomimetic motion is present is illustrated in Figure 4a.It can be observed that the penetrator with the expanded head design exhibits greater resistance than that without such a design.This may be attributed to the relatively smooth connection of the penetrator without the expansion design, which does not induce cavity expansion.However, with the introduction of oscillatory locomotion, this disparity narrows.At u = 1, the tip resistance of the design with the expanded head is slightly greater than that without the expanded head.At u = 4, the tip resistances of the two designs are indistinguishable.As depicted in Figure 4a, there is an increase in tip resistance for all cases with a higher penetration depth.Nonetheless, the integration of the lateral oscillation in the penetration process led to a decrease in tip resistance; and a higher oscillation rate corresponded to a lower tip resistance.The results distinctly indicate that the biomimetic head oscillation can effectively diminish the tip resistance force.Here, a period defined as the process wherein the penetrator moves from a vertical position to the right direction, reaching the maximum angle, then reverses back to the vertical position, subsequently moves to the left attaining the maximum angle, and finally returns to the vertical position.At u = 4, which implies a higher tip angular velocity, throughout the total penetration depth of 10 cm, there are approximately 45 periods, amounting to 180 reciprocating motions.Particularly, the fluctuation in data may be attributed to the limited particle contact and increased number of reciprocating motions induced by high angular velocity.
Figure 4b shows the shaft friction resistance force under different relative slip velocities.Similar to the tip resistance force, the shaft friction resistance force tends to increase with the penetration depth.This may be attributed to both a greater interaction area between the shaft and particles and the enhanced lateral earth pressure.It is worth noting that the penetration scenario at u = 4 experienced the least shaft friction during the process.

Force-chain network and particle velocity
The contact force chain network serves as an effective tool for investigating the propagation of forces throughout the penetration process.In Figure 5, it can be observed that the contact force chain networks for particles situated within a span of one cone diameter from the penetrator centerline are depicted as a planar projection onto a vertical section traversing the chamber center axis.It should be noted that although the angular velocities are different in the cases of u = 1 and u = 4, there are several positions throughout the penetration process where they are at the same depth and in a vertical position.Here, an intermediate depth (depth = 0.07 m) after complete penetration of the cone into the soil body has been selected to study the distribution of the force chain network.To underscore the variability in the propagated contact force concomitant with the penetrator kinematics, several measures are employed: (1) forces below 0.2 N are represented in a light grey shade; (2) the width of the force chains corresponds to their magnitude, with a color gradient transitioning from blue to red; (3) a consistent color scale is used for all force chain networks, enabling straightforward comparisons across different cases.
From Figure 5, it can be observed that at u = 0, the force chains are extensively distributed around the entire tip and expand outward.At u = 1 and u = 4, the distribution of strong force chains is primarily concentrated on the right side, as the penetrator swings to the right, compressing the soil body on the right side.It can be observed that the distribution of strong force chains is the least at u = 4, and it is maximum in pure penetration (u = 0).Interestingly, with biomimetic oscillation, the force chains tend to distribute horizontally, which is markedly different from pure penetration.
One of the characteristics of biomimetic head oscillation is that it applies periodic disturbances to the surrounding soil body.Our interest lies in the variations of force chains at different positions within a biomimetic motion cycle.A typical dynamic penetration cycle after the cone fully emerged was captured for a visual understanding of the dynamic penetration process.Figure 6 illustrates the variation in the force chain during one oscillation cycle of the penetrometer at a moderate depth (depth = 0.07m) with u = 4.The oscillation angle is defined as 0 degrees when positioned vertically.When it is on the right side, the angle is positive, and when on the left side, the angle is negative.In this study, the oscillation angle can reach a maximum of 5 degrees to the left and the right.As the penetrator swings from its vertical position to the right, the force chain is predominantly concentrated on the right side of the cone, indicating compression on the right side of the soil mass.The force chain on the right intensifies as the oscillation angle increases, reaching the maximum value when the angle is at its peak.Upon initiating the return motion to the left, the force chain on the right diminishes rapidly.From the second picture of the second row in Figure 6, significant gaps can be observed, suggesting limited particle contact.When the pendulum movement just begins to the left, the force chain on the left side is weak.This suggests that the back-and-forth oscillations cause loosening of the particles.However, as the swing to the left continues, the force chain on the left side progressively strengthens until it returns to the vertical position, where the force chain on the left reaches its peak, completing one periodic For a clear eluciation of the dynamic effects of oscillation on the granular soil system, the particle velocity field around the cone at a medium depth under different relative slip velocities is shown in Figure 7.In Figure 7(a), with the downward progression of the penetrator, the granular particles experience a relatively uniform radial displacement, suggesting an isotropic compression.However, in Figures 7(b) and 7(c), given the cone's rightward oscillation motion while maintaining a vertical advancement, the particles on its right side are mainly affected by the momentum of the prior movement, resulting in a rightward trajectory.The particles on the left demonstrate a tendency to gravitate downwards, adhering to the cone's left oblique facet.Notably, a correlation is observed wherein an escalation in the relative slip velocity augments the velocity of particles on the right, with their trajectory becoming increasingly horizontal.Figure 8a shows the velocity field of particles around the cone as the penetrator swings from a vertical position to its maximum angle to the right direction at a medium depth.As the oscillation angle increases, an increasing number of particles on the right side is mobilized, and the affected area gradually expands.Figure 8b depicts the process of the penetrator moving back to the vertical position from the left.It can be observed that for a certain period after the oscillation direction changes, there is a sudden drop in the velocity around the particles.Figures 8c and 8d show the motion trajectory of the particles on the right side of the cone as they just reach the maximum swing angle to the right and as they start to move back, respectively.It can be observed that the direction of motion of the particles on the right side has deviated.This result is consistent with the previous results on force chains, indicating that the oscillatory movement disturbs the particles.

Conclusion
In this study, two types of penetrators were modeled inspired by the burrowing techniques observed in worm lizards: one with an expanded joint and another with an inscribed joint.The simulation experiments were performed using the DEM to analyze the performance of the penetrator burrowing into a granular medium under different relative slip velocities.The impact of the biomimetic head oscillation was quantified by contrasting parameters such as tip resistance, evolution of force chain networks, and velocity field.The results indicate that the oscillatory movement can reduce the difference in tip resistance force between the two designs.The oscillatory disruption of the granular medium led to the breakage of force chains, subsequently reducing penetration resistance.The faster the oscillation, the lesser the resistance.
In Yong and Tao's research [19], it was discovered that awn-inspired rotation can effectively reduce penetration resistance.The awn-inspired rotation revolves around the axis of the penetrator, and both the cone and shaft rotate together.In contrast, the lateral oscillation is perpendicular to the axis of the penetrator in the direction of rotation, and only the cone is swinging.Although the locomotion modes are different, based on the preliminary research of this paper, lateral oscillation is also effective in reducing penetration resistance.In the research on awn-inspired rotation, the mechanism of penetration resistance reduction was further clarified by analyzing the particle-penetrator contact data, such as contact forces, contact numbers, and contact angles [19].These analytical methods are also applicable to this study.During the design process, power consumption must be considered because torque and energy are essential to achieve the intended locomotion, and it is important to evaluate the trade-off between energy expenditure and the reduction in resistance.In this study, the oscillation angle was limited to 5 degrees, as the oscillation angle determines the disturbance range and scales of soil particles.A broader range of combinations of oscillation angles and relative slip velocities should be explored in future research to reveal the impact of bio-inspired oscillation on the penetration process.

2 .Figure 3 .
Figure 3. (a) Penetrator with an expanded joint; (b) Penetrator with an inscribed joint; (c) Penetration test sample and the penetrator with an expanded joint, located 0.01 m above the top surface of the sample.

Figure 4 .
Penetration force under different relative slip velocities (a) Tip resistance force with an expanded joint and an inscribed joint; (b)Shaft friction force with an inscribed joint.
penetrator with an expanded joint penetrator with an incribed joint