All of the abalones Haliotis discus hannai in the experiment are artificially cultured and bought from a marine aquaculture plant located at the coastal region in Qingdao of China. These alive abalones are selected with the length approximately 5 cm. The abalones are fed in a 480 l tank which is equipped with a thermostat to form a filtering and water circulating system. The temperature of water in the tank is 19 ± 0.5°C. The sea water is made of fresh water and sea salt. The rectangular glasses with the size of 200 mm³ × 200 mm³ × 8 mm³ are used as substrates on which the abalones are raised. All of the substrates are placed in cages which are suspended in the tank. To make sure that each abalone could adapt to the new environment, all the individuals are held in the tank for seven days at least. The abalone is fed with kelp every other three days before the experiment to ensure that all the abalones are healthy (Li et al., 2018a; Zhang et al., 2019; Zhang et al., 2020).

The adhesive strength measurement of abalone is conducted on the universal testing machine (UTM–1432, Cheng De Jin Jian Testing Instrument Co. Ltd.). Firstly, a self-developed three-pronged steel jaw, which is designed to hold the abalone shell, is clamped by the upper fixture of the machine. And the substrate on which the abalone adheres is fixed on the sample stage. The pulling force is applied to pull the animal from the substrate with the velocity of 20 mm/min, which can be seen as a quasi-static load (Li et al., 2018b; Zhang et al., 2019). And the value of adhesion strength could be recorded by the machine.

The experiment conducted in a self-assembled circulatory system consists of a transparent cuboid aquarium with the volume of 0.8 × 0.6 × 0.5 m³, submersible pumps with various displacements and water channels with the size of 0.1 × 0.1 × 1 m³. Flowing in the water channel, the sea water with the salinity of 1.024 is pumped from the aquarium and flows back to the aquarium. In order to reduce turbulence, a rectifying net is installed near the entrance of the channel.

The number of abalone is 43, all samples are divided into three groups. Before being scoured, three groups of abalone are put in the channel with three different initial postures, i.e. facing water with tail, head and the side of the body, shown in Figure 1A. And the water velocity gradually increases to the target to guarantee that each abalone could stretch its foot and generate adhesion on the channel surface. The scouring process under the same target velocity is repeated five times. And each process is kept for at least 30 min. The number of abalones of each posture is recorded after each test. Then the probability p of these three postures is the mean value of five repeated experiments. Then we change the target velocity of water flow and repeat the same procedure.

We use the commercial software ABAQUS to simulate the pulling off process of abalone from the substrate. Both of the substrate and the abalone are considered as isotropic materials. The Young’s modulus of the abalone foot and shell are 1 MPa and 20 GPa respectively (Menig et al., 2000; Zhang et al., 2019). The Poisson’s ratios of the foot and the shell are 0.16 and 0.3 respectively. For convenience of calculation, the substrate, includes the trough and obstacle, could be treated as a rigid body in simulation. All the substrates are set as the fixed boundary in simulation. The density of water, the abalone foot and the shell are 1,024, 1,500, and 2,700 kg/m³ (Zhang et al., 2020). The foot and shell of abalone is tied via a small area (about 36 mm²) on the top surface of the foot.

The Eulerian and Lagrangian grids are used in liquid and solid parts respectively. The velocities of liquid area walls are set as that the vertical component is zero to avoid the penetration from the walls. The entrance boundary is set as the velocity condition, and the exit boundary is set as the Eulerian boundary with “nonreflecting” to avoid liquid reflection. In order to reduce the calculation, the adhesion between the abalone foot and the substrate is set as the “cohesive behavior”, as the mucus layer is very thin. The contact between solid and liquid is set as the “general contact”. The number of element is 17,839, which consists of 1671 C3D4 elements (abalone foot and shell), 168 C3D8R elements (substrate) and 16,000 EC3D8R elements (liquid).

In water, three potential postures of the abalone might occur to deal with the water flow. When the abalone faces water with its tail, head and side body, the postures are named as posture 1, posture 2 and posture 3 respectively, which are shown in Figure 1A. The probability for these three postures p with respect to the water velocity v is demonstrated in Figure 1B. It can be observed that, if the velocity is in the range from 0.5 to 2 m/s, the probability of posture 2 is the biggest, and that of posture 3 is the smallest. This indicates that the creature tends to face the water current with its head when the water is in a low velocity. However, with the increase of the velocity, the probability of posture 2 becomes the smallest, especially after v = 6 m/s. On the contrary, the probability of posture 1 increases and it is bigger than that of posture 2 after v = 2 m/s. It is guessed that, under the condition of low speed of water, the abalone can capture necessary information about the water under posture 2. However, when the water has a big velocity it may produce an impact on the abalone, and the abalone will modulate the posture to avoid the impact of water. In addition, the probability of posture 3 fluctuates with the increase of flow velocity, and its values are maintained at about 21%, which are smaller than those of posture 1 throughout the whole process. This is the reason that we have seldom observed posture 3 of abalone during water flow.

We then use the finite software ABAQUS to simulate the stress field of abalone and the flow field of water. Firstly, at three typical velocities, i.e. the submarine flow velocity (v = 0.5 m/s), the speed of ship (v = 15.43 m/s) and the speed of speedboat (v = 22 m/s), the stress cloud diagrams of abalone pedal are shown in Figure 2. The von Mizes stress of the pedal is defined as σ p = ( σ x − σ y ) 2 + ( σ y − σ z ) 2 + ( σ z − σ x ) 2 + 6 τ x y 2 + 6 τ y z 2 + 6 τ z x 2 2 , (1) where σ x , σ x , σ x , τ x y , τ x y , and τ x y are the stress components. Generally, the maximum stress of the pedal σ _pmax increases by 2.59–3.29 times when the velocity increases from 0.5 to 22 m/s for all of the three postures.

When the fluid velocity v = 0.5 m/s, the maximum stress of posture 2 is the biggest in comparison with the two other postures, as shown in Figures 2A,D,G. This stress distribution is not beneficial for the abalone keeping posture 2, but in the experiment we observe that this posture has the highest probability. This phenomenon could be explained from the perspective of the physiological structure of the abalone. Indeed, the animal can capture various information through the antennae and eyes on its head (Wanichanon et al., 2004; Li et al., 2006), and its mouth can also filter algal debris from the current. Although the maximum stress is bigger than those of the other postures, posture 2 is used to deal with water flow, indicating that the abalone can adapt to this stress field conveniently.

Moreover, the locations of the pedal maximum stress for the three postures all change with the increase of the fluid velocity. In detail, when v = 0.5 m/s, the maximum stress appears at the junction between the shell and the foot, see Figures 2A,D,G. With the increase of the current speed, the maximum stress location has transferred to the surface impacted by water, as shown in Figures 2C,F,I. This means that, under the low velocity condition, it is the abalone shell that bears the water impact. However, when the flow velocity further increases, the abalone shell is lifted slightly by water, and thus the abalone pedal is impacted directly by water.

In addition, more cases of the abalone under different fluid velocities are also simulated via FEM. For convenience, the Reynold number is defined as Re = ρ ν L μ , (2) where ρ is the water density, L is the characteristic length of the abalone, and μ is the kinematic viscosity of water (with the value of 0.001 Pa herein). Then the dependence relationship between the maximum stress of the pedal and the Reynold number is demonstrated in Figure 3. Based on the stress field we can judge that, roughly the posture 1 is the best strategy in which the maximum stress of abalone foot is the smallest with the whole variation process of the Reynold number.

However, when the velocity is in the low range, such as when 0 < Re < 3 × 10⁵, the curves for the three postures are not monotonic. In order to explain this phenomenon, we give the velocity field distributed around the abalone. It can be noticed that there is a vortex for each case, as shown in Figures 4A,D,G, respectively. The vortex is associated with very complicated fluid dynamics, and it will cause the fluctuation of the curves on the pedal stress. The vortex gradually fades and even disappears with the increase of the flow velocity, as shown in Figures 4B,C,E,F,H,I. As a consequence, there are disturbances in the initial stage of the pedal stress curves and then the curves become monotonic at high Reynold number values.

As shown in Figure 3, the maximum stress of abalone pedal is σ pmax   =   19 . 28   MPa , which occurs in case of posture 2 when v = 26 m/s. The tolerant strength of the abalone pedal has already been measured as [ σ p ]   =   31 . 82   MPa (Zhang et al., 2019). Evidently, one has σ pmax < [ σ p ] . This means that although the fluid flow can bring impact on the abalone, its muscle cannot be broken and the abalone is still safe under the high speed flow.

Under the action of water flow, the impact is directly applied on the abalone shell. Although the shell looks much stiffer than the muscle, its experimental value was measured as [ σ s ]   =   700   MP (Menig et al., 2000), the velocity and pressure fields are different from those of the pedal. Therefore a similar strength check must be performed to ensure the reliability of analysis.

Based on the FEM simulation, the stress field of the shell for the above three postures is given in Figure 5. It can be seen that the maximum stress increases by 1.38–1.67 times when the velocity changes from v = 0.5 m/s to v = 22 m/s. Moreover, the maximum stress on the shell for posture 1 is the smallest, and that for posture 3 is the biggest when v = 0.5 m/s, v = 15.43 m/s, and v = 22 m/s. This again stresses that posture 3 is seldom observed in experiments.

The maximum stress of the shell is located at the side impacted by the water flow, except the case of posture 2 at v = 0.5 m/s. When v = 0.5 m/s, the maximum stress appears at the contralateral side of the impacted aspect of the shell, as during this situation one vortex appears at the tail of the shell. Furthermore, the curves on the maximum stress always fluctuate at low Re values (see Figure 6), and this phenomenon may be due to the appearance of vortex, as shown in Figures 4A,D,G. The curves grow monotonically with the increase of Re, which is the result of the reduction of the vortex, as shown in Figures 4C,F,I.

For the strength check, we select the maximum stress value of the shell shown in Figure 6 as σ smax   =   500   MPa , which is much higher than that of the pedal. This value corresponds to the small area under fluid impact in conjunction with the pedal, and the stress concentration must happen. Although this value is sufficiently huge, its value is smaller than the tolerant strength of the shell, i.e. σ smax < [ σ s ] . This condition ensures the safety of the shell under the action of fluid dynamics. We also find that the maximum stress value in posture 1 under high Re values, is actually the smallest among the three curves, see the red one in Figure 6. This may be one of the reasons that the abalone tends to face the high velocity fluid with its tail.

It can be easily imagined that, when the flow velocity increases continuously, the adhesion of the abalone on the substrate would fail. The critical cases that the abalone is detached from the substrate in these three postures, are thus investigated. Generally speaking, the energy required for detachment of the abalone pedal comes from the water current. For convenience of simplification, the kinetic energy of the muscle is ignored. As the resistance of the abalone, the kinetic energy varies not much even at the critical case.

According to the balance of energy, all the work W done by the current as well as the work W ₁ done by normal force in normal detachment experiment are converted into the strain energy U and used to overcome the interfacial energy E of the pedal-substrate interface, which can be expressed as W = W 1 = U + E , (3) The uniaxial tension experiment on the peeling process of the abalone is schematized in Figure 7A, and then the stress-strain curve is given in Figure 7B. The dimensionless stress is defined as σ / σ max in which σ and σ max are the normal stress and maximum stress of the abalone (along the pulling direction) in the stress-strain curve. According to the stress-strain curve, one exponential function can be fitted as σ σ max ( ε ) = 0.062 ⁡ exp ( 5 ε ) − 0.05162 , R 2 = 0 . 99 , (4) Thus, W1 can be deduced as W 1 = σ max A F h ∫ 0 ε F σ σ max ( ε ) d ε , (5) where h is the initial maximum height of the abalone, ε F is the strain when the abalone is pulled off from the substrate, and A F is the initial adhesive area.

The abalone is subjected to the effect of the flow, which consists of the lift force F L and the drag force F D : F L = 0.5 C L ρ A F v 2 , (6) F D = 0.5 C D ρ A D v 2 , (7) where C _L and C _D are the lift coefficient and drag coefficient respectively, and A _D is the frontal area which is measured as 3.5 cm² for posture 1, 2, and 5.5 cm² for posture 3. The work of water applied to the abalone can be written as W = F L U L + F D U D , (8) where U _L and U _D are the displacements of the abalone when it is peeled, which are obtained via simulation. The symbols C _L and C _D are affected by the characteristic length L of the abalone and the flow velocity. The values of C _L and C _D used in this study are obtained at Re ≈ 10⁵, and all of our experimental parameters fall in this range. Since the shape and size of abalone are similar to that of limpet, C _L and C _D are selected as 0.35 and 0.45 respectively (Denny et al., 1985).

As a consequence, the critical velocities of three postures are theoretically computed as v _c = 26.2 m/s for posture 1, v _c = 25.8 m/s for posture 2 and v _c = 23.02 m/s for posture 3. The results obtained via FEM simulation are v _c = 32 m/s for posture 1, v _c = 28 m/s for posture 2 and v _c = 26 m/s for posture 3 respectively. It can be seen that the errors between two results are 18.12% for posture 1, 7.86% for posture 2 and 11.46% for posture 3. These discrepancies mainly come from the simplification process and energy loss of the water flow, but the theoretical computation and the simulation results are on the same order. According to these results, posture 1 is the best strategy to avoid detachment from the substrate, which agrees with our experimental results.