Effect of internal damping on locomotion in frictional environments.

The gaits of undulating animals arise from a complex interaction of their central nervous system, muscle, connective tissue, bone, and environment. As a simplifying assumption, many previous studies have often assumed that sufficient internal force is available to produce observed kinematics, thus not focusing on quantifying the interconnection between muscle effort, body shape, and external reaction forces. This interplay, however, is critical to locomotion performance in crawling animals, especially when accompanied by body viscoelasticity. Moreover, in bioinspired robotic applications, the body's internal damping is indeed a parameter that the designer can tune. Still, the effect of internal damping is not well understood. This study explores how internal damping affects the locomotion performance of a crawler with a continuous, viscoelastic, nonlinear beam model. Crawler muscle actuation is modeled as a traveling wave of bending moment propagating posteriorly along the body. Consistent with the friction properties of the scales of snakes and limbless lizards, environmental forces are modeled using anisotropic Coulomb friction. It is found that by varying the crawler body's internal damping, the crawler's performance can be altered, and distinct gaits could be achieved, including changing the net locomotion direction from forward to back. We will discuss this forward and backward control and identify the optimal internal damping for peak crawling speed.

Pacific lamprey inspired climbing.

Snakes and their bio-inspired robot counterparts have demonstrated locomotion on a wide range of terrains. However, dynamic vertical climbing is one locomotion strategy that has received little attention in the existing snake robotics literature. We demonstrate a new scansorial gait and robot inspired by the locomotion of the Pacific lamprey. This new gait allows a robot to steer while climbing on flat, near-vertical surfaces. A reduced-order model is developed and used to explore the relationship between body actuation and the vertical and lateral motions of the robot. Trident, the new wall climbing lamprey-inspired robot, demonstrates dynamic climbing on a flat near vertical carpeted wall with a peak net vertical stride displacement of 4.1 cm per step. Actuating at 1.3 Hz, Trident attains a vertical climbing speed of 4.8 cm s-1(0.09 Bl s-1) at specific resistance of 8.3. Trident can also traverse laterally at 9 cm s-1(0.17 Bl s-1). Moreover, Trident is able to make 14% longer strides than the Pacific lamprey when climbing vertically. The computational and experimental results demonstrate that a lamprey-inspired climbing gait coupled with appropriate attachment is a useful climbing strategy for snake robots climbing near vertical surfaces with limited push points.

Cavitation Rheology of Model Yield Stress Fluids Based on Carbopol.

Measuring the surface tension of yield stress fluids has remained a critical challenge due to limitations of the traditional tensiometry techniques. Here, we overcome those limits and successfully measure the surface tension and mechanical properties of a model yield stress fluid based on Carbopol gels via a needle-induced cavitation (NIC) technique. Our results indicate that the surface tension is approximately 70 ± 3 mN/m, and is independent of the rheology of yield stress fluid over a wide range of yield stress values σy = 0.5-120 Pa. In addition, we demonstrate that a Young modulus smaller than E < 1 kPa can be successfully measured for Carbopol gels with NIC method. Finally, we present a time-resolved flow structure around the cavity in a host of yield stress fluids, and assess the impact of fluid rheology on the detailed form of flow around the cavity. Interestingly, prior to the critical point associated with cavitation, the yield stress fluid is weakly deformed suggesting that the measured surface tension data reflect the near equilibrium values. Beyond the critical point, the yield stress fluid experiences a strong flow that is controlled by both the critical pressure and the non-Newtonian rheology of the yield stress fluid.

Helical Locomotion in Yield Stress Fluids.

We report three stages for locomotion of a helical swimmer in yield stress fluids. In the first stage, the swimmer must overcome the material's yield strain to generate rotational motion. However, exceeding the first threshold is not sufficient for locomotion. Only when the viscous forces are sufficiently strong to plastically deform the material to a finite distance away from the swimmer will net locomotion occur. Once locomotion is underway in the third stage, the yield stress retards swimming at small pitch angles. Conversely, at large pitch angles, yield stress dominates the flow by enhancing swimming speed. Flow visualizations reveal a highly localized flow near the swimmer in yield stress fluids.

Flapping dynamics of an inverted flag behind a cylinder.

The inverted flag configuration is inspired by biological structures (e.g. leaves on a tree branch), showing rich dynamics associated with instabilities at lower flow speeds than the regular flag configuration. In the biological counterpart, the arrangement of leaves and twigs on foliage creates a complex interacting environment that promotes certain dynamic fluttering modes. While enabling a large amplitude response for reduced flow speeds is advantageous in emerging fields such as energy harvesting, still, little is known about the consequence of such interactions. In this work, we numerically study the canonical bio-inspired problem of the flow-structural interaction of a 2D inverted flag behind a cylindrical bluff body, mimicking a leaf behind a tree branch, to investigate its distinct fluttering regimes. The separation distance between the cylinder and flag is gradually modified to determine the effective distance beyond which small-amplitude or large-amplitude flapping occurs for different flow velocities. It is shown that the flag exhibits a periodic large amplitude-low frequency response mode when the cylinder is placed at a sufficiently large distance in front of the flag. At smaller distances, when the flag is within the immediate wake of the cylinder, the flag undergoes a high frequency-small amplitude response. Finally, the flag's piezoelectric power harvesting capability is investigated numerically and experimentally for varying geometrical and electrical parameters associated with these two conditions. Two separate optimal response modes with the highest energy output have also been identified.

Branching pattern of flexible trees for environmental load mitigation.

Wind-induced stress is the primary mechanical cause of tree failures. Among different factors, the branching mechanism plays a central role in the stress distribution and stability of trees in windstorms. A recent study showed that Leonardo da Vinci's original observation, stating that the total cross section of branches conserved across branching nodes is the optimal configuration for resisting wind-induced damage in rigid trees, is correct. However, the breaking risk and the optimal branching pattern of trees are also a function of their reconfiguration capabilities and the processes they employ to mitigate high wind-induced stress hotspots. In this study, using a numerical model of rigid and flexible branched trees, we explore the role of flexibility and branching patterns of trees in their reconfiguration and stress mitigation capabilities. We identify the robust optimal branching mechanism for an extensive range of tree flexibility. Our results show that the probability of a tree breaking at each branching level from the stem to terminal foliage strongly depends on the cross section changes in the branching nodes, the overall tree geometry, and the level of tree flexibility. Three response categories have been identified: the stress concentration in the main trunk, the uniform stress level through the tree's height, and substantial stress localization in the terminal branches. The reconfigurability of the tree determines the dominant response mode. The results suggest a very similar optimal branching law for both flexible and rigid trees wherein uniform stress distribution occurs throughout the tree's height. An exception is the very flexible branched plants in which the optimal branching pattern deviates from this prediction and is strongly affected by the reconfigurability of the tree.

Bridge the gap: correlate face mask leakage and facial features with 3D morphable face models.

BACKGROUND: Face masks have been proven to be effective in protecting the public against airborne transmitted diseases when fitted appropriately. However, for homemade cloth masks and surgical masks, the fit is often poor, allowing viruses to escape through the gap. OBJECTIVE: This work aims to identify the correlation between the mask leakage, mask configurations, and individual's facial features. METHODS: A novel locally morphing 3D face model, and a minimum-energy-based mask deployment model are used to systematically examine the mask fit for a large cohort of exemplars. RESULTS: The results show that the mask size and tuck-in ratio, along with selective facial features, especially nose height and chin length, are key factors determining the leakage location and extent. A polynomial regression model is presented for mask fitness based on localized facial features. SIGNIFICANCE: This study is a complete pipeline to test various masks on a wide range of faces with controlled modification of distinct regions of the face, which is difficult to achieve with human subjects, and provide knowledge on how the masks should be designed in the future. IMPACT STATEMENT: The face mask "fit" affects the mask's efficacy in preventing airborne transmission. To date, research on the face mask fit has been conducted mainly using experiments on limited subjects. The limited sample size in experimental studies makes it hard to reach a statistical correlation between mask fit and facial features in a population. Here, we employ a novel framework that utilizes a morphable face model and mask's deployment simulation to test mask fit for many facial characteristics and mask designs. The proposed technique is an important step toward enabling personalized mask selection with maximum efficacy for society members.

One size fits all?: A simulation framework for face-mask fit on population-based faces.

The use of face masks by the general population during viral outbreaks such as the COVID-19 pandemic, although at times controversial, has been effective in slowing down the spread of the virus. The extent to which face masks mitigate the transmission is highly dependent on how well the mask fits each individual. The fit of simple cloth masks on the face, as well as the resulting perimeter leakage and face mask efficacy, are expected to be highly dependent on the type of mask and facial topology. However, this effect has, to date, not been adequately examined and quantified. Here, we propose a framework to study the efficacy of different mask designs based on a quasi-static mechanical model of the deployment of face masks onto a wide range of faces. To illustrate the capabilities of the proposed framework, we explore a simple rectangular cloth mask on a large virtual population of subjects generated from a 3D morphable face model. The effect of weight, age, gender, and height on the mask fit is studied. The Centers for Disease Control and Prevention (CDC) recommended homemade cloth mask design was used as a basis for comparison and was found not to be the most effective design for all subjects. We highlight the importance of designing masks accounting for the widely varying population of faces. Metrics based on aerodynamic principles were used to determine that thin, feminine, and young faces were shown to benefit from mask sizes smaller than that recommended by the CDC. Besides mask size, side-edge tuck-in, or pleating, of the masks as a design parameter was also studied and found to have the potential to cause a larger localized gap opening.

Drafting mechanisms between a dolphin mother and calf.

We numerically study the drafting mechanisms between a dolphin mother and her calf swimming near the free surface. Formation locomotion between the cetacean mother-calf pair provides a way for the mother to assist the calf in its locomotion. Depending on the age and size of the calf, it swims at neonate, echelon, and infant positions. At each position, the effects of the calf's size, swimming speed, proximity to the free surface and the formation pattern are investigated and the optimal configurations predicted by the model based on the swimming hydrodynamics are compared with previous observations. It is shown that the neonate position is the optimal formation for controlling the separation of the calf, and the echelon position is the most hydrodynamically efficient position in transferring the thrust force from the mother to the calf. The infant position, on the other hand, avoids the energy loss due to wave generation so that it improves the self-propulsion performance of an older calf.

Performance of synchronized fins in biomimetic propulsion.

By using a two-dimensional model of ray fins, we numerically investigate the thrust generation by closely-coupled fins with an immersed boundary approach. The concentration is on the performance enhancement through fin-fin interactions and the underlying vortex control mechanisms in three representative systems, a two-fin tandem configuration, a two-fin parallel configuration, and a three-fin triangular configuration. In all these systems the thrust generation can be significantly increased in comparison with single fins. Unlike previous studies of tandem fins, in which the gap and phase lag between the two fins were considered separately, our study shows that the dynamics of the system is determined by a parameter that combines these two (the global phase difference). The optimal performance occurs as this parameter is around π (destructive mode), and the worst performance occurs when it is around 0 (constructive mode). Interestingly, contrary to the vorticity cancellation scenario implied by its name, our simulations show that in the destructive mode there is in fact a wake re-organization mechanism, during which vortices with the same rotational direction shed from the two fins are attracted towards each other and merge. Subsequently, the wake downstream becomes a strong and well-organized reverse Kármán vortex street, which explains the increased thrust. In the parallel system, the best performance occurs in cases when the two fins are in opposites phases. Both the thrust and efficiency increase as the gap between the fins decreases, until a symmetry-breaking instability occurs in the wake and the efficiency starts plunging due to the increase in lateral force generation. In the triangular formation, the highest thrust generation also occurs in the destructive mode. However, no further increase in performance is observed compared with the tandem system.

Numerical simulation of a pectoral fin during labriform swimming.

We numerically examine the fluid-structure interaction and force generation of a skeleton-reinforced fin that geometrically, structurally and kinematically resembles the pectoral fin of a fish during labriform swimming. This fin contains a soft membrane with negligible bending stiffness and 12 embedded rays (modeled as beams). A potential flow-based boundary element model is applied to solve the fluid flow around the fin, in which the vorticity field is modeled as thin vorticity sheets shed from prescribed locations (the sharp trailing edge). The fin motion is actuated by dorsoventral and anteroposterior rotations of the rays (the motion of each ray is controlled individually), as well as pitching motion of the baseline. Consequently, the fin undergoes a combination of flapping (lift-based) and rowing (drag-based) motions typical in labriform swimming. The fin motion contains two strokes: a recovery stroke and a power stroke. The performance of the fin depends upon kinematic parameters such as the Strouhal number, the phase lag between rays, the pitching motion of the baseline and the passive deformations of the rays. The most interesting finding is that the strengthening of the ray at the leading edge plays a pivotal role in performance enhancement by reducing the effective angle of attack and decreasing the power expenditure during the recovery stroke.

Fluid-structure interactions of skeleton-reinforced fins: performance analysis of a paired fin in lift-based propulsion.

We investigate the thrust generation capacity of a thin foil consisting of a membrane strengthened by embedded rays that is geometrically, structurally and kinematically similar to pectoral fins of bony fishes during lift-based labriform locomotion. Our numerical model includes a fully nonlinear Euler-Bernoulli beam model of the skeleton and a boundary-element model of the surrounding flow field. The fin undergoes a dorso-ventral flapping activated by rotations of the rays. Both the trailing edge vortices (TEV) and the leading edge vortices (LEV) are accounted for and modeled as shear layers. The thrust generation and propulsion efficiency are examined and documented. Our results show that synchronization of rays is pivotal to the performance of the system. A primary factor that determines the performance of the fin is phase lags between the rays, which create variations of the effective angle of attack at the leading edge as well as shape changes throughout the fin surface. Structural flexibility of the rays leads to passive deformations of the fin, which can increase the thrust generation and the propulsion efficiency.

Propulsion performance of a skeleton-strengthened fin.

We examine numerically the performance of a thin foil reinforced by embedded rays resembling the caudal fins of many fishes. In our study, the supporting rays are depicted as nonlinear Euler-Bernoulli beams with three-dimensional deformability. This structural model is then incorporated into a boundary-element hydrodynamic model to achieve coupled fluid-structure interaction simulation. Kinematically, we incorporate both a homocercal mode with dorso-ventral symmetry and a heterocercal mode with dorso-ventral asymmetry. Using the homocercal mode, our results demonstrate that the anisotropic deformability of the ray-reinforced fin significantly increases its capacity of force generation. This performance enhancement manifests as increased propulsion efficiency, reduced transverse force and reduced sensitivity to kinematic parameters. Further reduction in transverse force is observed by using the heterocercal mode. In the heterocercal model, the fin also generates a small lifting force, which may be important in vertical maneuvers. Via three-dimensional flow visualization, a chain of vortex rings is observed in the wake. Detailed features of the wake, e.g. the orientation of the vortex rings in the heterocercal mode, agree with predictions based upon particle image velocimetry (PIV) measurements of flow around live fish.