The mechanics of abalone crawling on sharp objects without injury

Despite the soft appearance of their feet, abalones can crawl quickly on sharp objects. Tests using rough substrates aligned with blades or posts found that the animal has two adaptations to guarantee its safety on these surfaces. Mechanical compression tests showed that the abalone foot muscle is inherently robust and can resist penetration by sharp objects. A finite element simulation indicated that to avoid being pierced, abalone controls the shape of its foot to wrap it around sharp objects, thereby greatly reducing the stress concentration. These analyses may aid the engineering of new materials and devices for fields including soft robotics and aircraft.

www.nature.com/scientificreports www.nature.com/scientificreports/ sides. The contact position of the abalone on the blade indicates that the blade edge was clamped by the abalone, with the blade indenting the sole by around 3 mm. After being pulled from the blades, some grooves (around 2.13 mm deep) remained on the surface of the sole (Fig. 1c), but they disappeared after several minutes without leaving any injury (Fig. 1d). Similarly, a bottom view of the abalone foot in contact with the cylindrical posts ( Fig. 2c) shows the muscle encircling the posts and adhering to their side surfaces. The posts indented beyond the line of the sole by approximately 2.33 mm and also left no injury on the abalone foot after the animal's removal from either of the post types.
The following analysis outlines the mechanics of the abalone's avoidance of injury on these sharp surfaces. As soon as the abalone is placed on these sharp surfaces it has not had time to respond and modulate its posture, and thus the contact surface is approximately planar. Under this assumption, the pressure on the contact area of the foot can be estimated as where G a is the gravitational force of the abalone body, F a is its buoyancy, n i is the number of objects in contact with the abalone foot, and A i is the real contact area of the foot with a single object. Subscript i = 1, 2, or 3 is adopted to indicate blades, cylindrical posts, or pointed posts, respectively. Although the blades or pointed posts are sharp, there is in practice always a finite contact surface between each of them and the abalone foot, which is either rectangular or circular. For blades of width b and length l, this area, A 1 , is expressed as bl (Fig. 1a). For the cylindrical and pointed posts, the areas A 2 and A 3 are given as πr i 2 , where r i is the contact radius between the abalone and the solid. In addition, we also calculated a more accurate estimate via an FEM simulation to identify the failure mechanism of the foot muscle's structure and make some comparisons (Fig. 3). Therefore, without loss of generality, the abalone foot material is modelled as a linearly elastic Hookean material. Figure 3a-c show the non-uniform distributions of the von Mises stress, σ eqi (i = 1, 2, 3) on the foot, and σ eqi is greatest on the periphery of the contact area. The maximum vertical stresses, taken here as the von Mises stress, calculated by FEM are different from those predicted by Eq. (1), but they are of a similar order of magnitude (Table 1). This is because the simplified model in Eq. (1) does not consider stress concentration, whereas the FEM simulation is based on a more rigorous three-dimensional model.
The first possible reason that abalone can crawl safely on sharp surfaces is that the maximum equivalent stress of the muscle is within the limit stress, namely, the foot is sufficiently robust to resist the external forces. A series of ultimate strength tests on the foot in contact with each of the three sharp surfaces generated the force-displacement curves in Fig. 4, which show two stages. In the first stage, the force increases slowly because the contact of the sharp surfaces with the soft muscle of the abalone is accompanied by a large deformation of the muscle. In the second stage, the contact attains a stable state, and the muscle still has sufficient capability to resist the external force. As the force gradually increases further to its peak of F maxi , the sole's surface is finally broken and the pressure attains the tolerant strength, [p i ]. The displacements at the critical peaks for each of the three sharp surfaces (i = 1, 2, 3) are 6.33, 4.19, and 4.53 mm, respectively. The tolerant strength is defined as The values of [p i ] are derived from these force-displacement curves, and are far greater than the values of the maximum stresses for the three substrates, i.e.
This relation indicates that the abalone is safe on these sharp surfaces as its sole does not collapse. When the abalone crawls, its acceleration has dynamic effects and increases the stress generated by the contact. The short period of acceleration is several seconds, and the abalone reaches a velocity, v, of 39.1 cm/min. The acceleration and dynamic force can be estimated as ~0.1 cm s −2 and ~10 −4 N, respectively. Furthermore, undersea currents also affect the stress concentration. Consequently, the strength condition in Eq. (3) may not be sufficient to guarantee the safety of the abalone in practice, and there are likely to be other strategies that abalones use.
Experiments have found that abalones wrap their highly flexible feet around sharp objects on substrates. Abalones use the antennae on their heads to obtain information about the morphology of a substrate before they traverse it in order to judge whether the substrate is dangerous 31,32 . Once the animal notices that these sharp objects are potentially dangerous, it protects itself by adhering to the side surface of the objects. However, it is not known whether the tip of a sharp object touches the abalone foot directly. Thus, there are two possible contact states between the abalone and a sharp object. In contact state I, the abalone foot directly touches the solid at the tip of the sharp object, fully wrapping around it. In contact state II, the abalone does not touch the tip of the sharp object, separating its foot slightly (0.3 mm in the simulation) from the object. In this case, the foot still adheres to the side surfaces of the object.
For adhesion to the three substrates tested here, the stress fields for contact states I and II, σ i eq I and σ i eq II (i = 1, 2, 3), respectively, were quantitatively calculated by FEM (Fig. 3). The data in Table 1 show that the stress values for contact state I are greater than those for contact state II, especially for the cylindrical posts. This is because the muscle avoided the sharp edges of the blades or posts, which reduced the stress concentration. In addition, the FEM values of the von Mises stress for contact states I and II are much smaller than the corresponding values in the initial contact states, namely, σ i eq II < σ i eq I < σ i eq . The percentage reduction in von Mises stress for contact states I and II, φ i I and φ i II , respectively, are defined as www.nature.com/scientificreports www.nature.com/scientificreports/ The values are calculated as φ i I = 92.69%, 85.73%, and 99.26%; and φ i II = 94.24%, 98.41%, and 99.47% for i = 1, 2 and 3, respectively. This wrapping strategy appears to decrease the stress concentration greatly compared with the initial contact state, and thus allows the abalone to crawl on a broader range of sharp surfaces.  www.nature.com/scientificreports www.nature.com/scientificreports/ In conclusion, we examined the special ability of the abalone to protect itself when crawling on sharp substrates. We found that the muscle of the abalone's foot is sufficiently strong to bear the pressure caused by sharp objects. In addition, the creature can deform its foot to avoid being pierced by sharp objects. To reduce the stress concentration, the abalone encircles the dangerous area of a sharp object using its flexible foot, thereby reducing the stress by more than 90%. We hope these analyses will help engineers to develop new materials and devices in fields such as soft robotics and aircraft.

Methods
A camera (D720, Nikon, 4000 × 6000 dpi) was used to record the crawling and adhesion of abalone on sharp substrates. The shapes of the substrate surfaces, as observed by an extended depth-of-field microscope (LY-WN-YH3D, Cheng Du Li Yang Precision Machinery Co. Ltd.), were used to calculate the vertical stress of the abalone foot at the moment of contact with the substrate. Commercial software (ABAQUS 6.14, Dassault Systèmes) accurately computed the equivalent stress when the abalone was adhered to the substrate.
Abalone and sharp objects. The abalones considered here were Haliotis discus hannai, an edible variety from the coastal area of Qingdao City, China. Ten 2.5-year-old cultivated abalone were tested. The mean body length was 6.8 ± 0.7 cm, and the body weights ranged from 48 to 52 g. Abalones were kept in individual transparent aquariums (80 × 60 × 100 cm 3 ), and were fed kelp every three days. The tanks were equipped with a chiller and a filtration system, and were maintained at 19 to 20 °C.
Three substrates were created from sharp objects: blades (Fig. 1a), cylindrical steel posts (Fig. 2a), and pointed posts (Fig. 2b). The blades were 100 mm long, 18 mm wide, and 0.5 mm thick, and were placed 3.6 mm apart. The included angle of each blade (the angle between the two side surfaces) was α = 13.6°, and although sharp, the edge was regarded as a rectangle of width b = 0.034 mm and length l = 100 mm. The cylindrical steel posts were of height h 2 = 25 mm and radius r 2 = 0.5 mm. The pointed posts were of height h 3 = 30 mm, conical angle β = 37.7°, and tip radius r 3 = 0.22 mm. Both types of posts were placed 10 mm apart. The blades and posts were washed and sterilized before being fixed at the bottom of the tank. tolerance strength testing. The soles of two abalone were compressed with a universal testing machine (UTM-1432, Cheng De Jin Jian Testing Instrument Co. Ltd.). After immersion in 5% MgCl 2 in seawater 33,34 , the abalone foot was first cut off along the attachment muscle, and placed on the platform of the material testing machine. Substrates with the three types of sharp object were then fixed to the punch of the testing machine, which moved them downward into the abalone. The loading velocity was set as 20 mm/min, which ensured the experiment was in a quasi-static state 35,36 . Ten different positions on the abalone foot surfaces were measured. The experiments were carried out at room temperature, around 24 °C. Force-displacement curves were recorded by the testing machine.
Young's modulus and poisson's ratio testing. Five cuboid (30 × 8 × 6 mm) samples, cut from the sole of an anaesthetized abalone, were clamped in the universal testing machine (UTM-1432). The loading velocity was kept at 20 mm/min, and stress-strain curves in the longitudinal direction were obtained. The Young's modulus was measured as E a = 0.994 ± 0.32 MPa, and the Poisson's ratio was ν = 0.16 ± 0.09. FeM simulation. ABAQUS 6.14 simulated the contact between the abalone foot and the sharp substrates; only one quarter of the configuration was calculated due to its symmetry. The blade, both posts and the abalone www.nature.com/scientificreports www.nature.com/scientificreports/ were considered as isotropic materials. The Young's modulus of the steel used in the blades and posts was 21,000 MPa, which was much greater than that of the abalone. The simulation used the element C3D8R. The contact approach between the substrate and the abalone was set as hard contact. The mesh numbers for modelling the abalone on the blade were 2400 for the blade, 750,000 for the foot before contact, and 68,628 after full adhesion. Those for the cylindrical posts were 4800 for the cylinder, 680,000 for the foot before contact, and 655,312 after full adhesion. Those for the pointed posts were 3406 for the post, 364,000 for the foot before contact, and 196,640 after full adhesion.