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We present theory and simulations of the well-known waving, coiling and skewing patterns exhibited by roots of Arabidopsis thaliana when grown on inclined agar substrates. By modelling growing slender organs as Cosserat rods that mechanically interact with the environment, our simulations confirm previous hypotheses of waving and coiling arising from the combination of active gravitropism and passive root-plane interactions. Skewing is instead related to intrinsic twist due to cell file rotation. Numerical investigations are outfitted with an analytical framework that consistently relates transitions between straight, waving, coiling and skewing patterns with tilt angle. Simulations are found to corroborate theory and recapitulate a host of reported experimental observations, thus providing a systematic approach for studying in silico interactions of plant organs with their environment.

Soft robots are notoriously hard to control. This is partly due to the scarcity of models and simulators able to capture their complex continuum mechanics, resulting in a lack of control methodologies that take full advantage of body compliance. Currently available methods are either too computational demanding or overly simplistic in their physical assumptions, leading to a paucity of available simulation resources for developing such control schemes. To address this, we introduce Elastica, an open-source simulation environment modeling the dynamics of soft, slender rods that can bend, twist, shear, and stretch. We couple Elastica with five state-of-the-art reinforcement learning (RL) algorithms (TRPO, PPO, DDPG, TD3, and SAC). We successfully demonstrate distributed, dynamic control of a soft robotic arm in four scenarios with both large action spaces, where RL learning is difficult, and small action spaces, where the RL actor must learn to interact with its environment. Training converges in 10 million policy evaluations with near real-time evaluation of learned policies.

Viscous streaming refers to the rectified, steady flows that emerge when a liquid oscillates around an immersed microfeature, typically a solid body or a bubble. The ability of such features to locally concentrate stresses produces strong inertial effects to which both fluid and immersed particles respond within short length (O(100) microns) and time (milliseconds) scales, rendering viscous streaming arguably the most efficient mechanism to exploit inertia at the microscale. Despite this potential, viscous streaming has been investigated in rather narrow conditions, mostly making use of bodies of uniform curvature (cylinders, spheres) for which induced flow topologies are constrained to only two regimes, classically referred to as single and double layer regimes. This severely limits the scope of potential applications, and sits in stark contrast to inertial focusing (the approach that perhaps has most defined the field of inertial microfluidics), where instead boundaries with multiple curvatures have long been utilised to magnify inertial effects, expand design space, and enable novel applications. Here, we demonstrate that a multi-curvature approach in viscous streaming dramatically extends the range of accessible flow topologies. We show that numerically predicted, but never experimentally observed, streaming flows can be physically reproduced, computationally engineered, and in turn used to enhance particle manipulation, filtering and separation in compact, robust, tunable and inexpensive devices. Overall, this study provides an avenue to unlock the utility of viscous streaming with potential applications in manufacturing, environment, health and medicine, from particle self-assembly to microplastics removal.

We report analytical solutions of a problem involving a visco-elastic solid material layer sandwiched between two fluid layers, in turn confined by two long planar walls that undergo oscillatory motion. The resulting system dynamics is rationalized, based on fluid viscosity and solid elasticity, via wave and boundary layer theory. This allows for physical interpretation of elasto-hydrodynamic coupling, potentially connecting to a broad set of biophysical phenomena and applications, from synovial joint mechanics to elastometry. Further, obtained solutions are demonstrated to be rigorous benchmarks for testing coupled incompressible fluid–hyperelastic solid and multi-phase numerical solvers, towards which we highlight challenging parameter sets. Finally, we provide an interactive online sandbox to build physical intuition, and open-source our code-base.

In the face of humanity's increasing problems of water insecurity, useful lessons in moisture management may be learned from organisms living in extreme climates. The Namib desert beetle uses its own body to extract water, in the form of fog, from the wind, and its dorsal features have inspired designs based on controlled wettability. Here, we revisit the beetle's physical adaptations from the fluid dynamics perspective of aerosol impaction. Coupled experiments and simulations show that subtle modulations in shape and texture create large gains in water harvesting performance by encouraging droplets to `slip' toward targets at the millimetric scale, and by disrupting boundary and lubrication layers effects at the microscopic scale. Our results offer a lesson in biological fog collection, and design principles for controlling particle separation in a variety of contexts.

Recent studies on viscous streaming flows in two dimensions have elucidated the impact of body curvature variations on resulting flow topology and dynamics, with opportunities for microfluidic applications. Following that, we present here a three-dimensional characterization of streaming flows as functions of changes in body geometry and topology, starting from the well-known case of a sphere to progressively arrive at toroidal shapes. We leverage direct numerical simulations and dynamical systems theory to systematically analyse the reorganization of streaming flows into a dynamically rich set of regimes, the origins of which are explained using bifurcation theory.

Natural creatures, from fish and cephalopods to snakes and birds, combine neural control, sensory feedback and compliant mechanics to effectively operate across dynamic, uncertain environments. In order to facilitate the understanding of the biophysical mechanisms at play and to streamline their potential use in engineering applications, we present here a versatile numerical approach to the simulation of musculoskeletal architectures. It relies on the assembly of heterogenous, active and passive Cosserat rods into dynamic structures that model bones, tendons, ligaments, fibers and muscle connectivity. We demonstrate its utility in a range of problems involving biological and soft robotic scenarios across scales and environments: from the engineering of millimeter-long bio-hybrid robots to the synthesis and reconstruction of complex musculoskeletal systems. The versatility of this methodology offers a framework to aid forward and inverse bioengineering designs as well as fundamental discovery in the functioning of living organisms., Natural creatures, from fish to snake and birds, combine neural control, sensory feedback and compliant mechanics to operate across uncertain environments. Here the authors present a versatile modeling approach to the dynamic simulation of their architectures based on the assembly of Cosserat rods.

Significance Biohybrid machines have been developed using muscles to actuate soft robotic structures. We envision that the integration of neurons into the embodiment of such systems can transform them into intelligent machines which, for instance, could use sensory neurons to detect environmental cues then adaptively respond and orchestrate various motor patterns through their neural circuitry. However, achieving such sensory-motor modalities relies on the ability of neural units to command muscle activity, making actuation through motor neurons the first milestone. Here, we achieve this milestone and demonstrate neuromuscular actuation of a biohybrid swimmer. This paves the way for the development of biohybrid embodied platforms as models to gain deeper understanding of motor control, with potentially broad impact in robotics, bioengineering, and health., The integration of muscle cells with soft robotics in recent years has led to the development of biohybrid machines capable of untethered locomotion. A major frontier that currently remains unexplored is neuronal actuation and control of such muscle-powered biohybrid machines. As a step toward this goal, we present here a biohybrid swimmer driven by on-board neuromuscular units. The body of the swimmer consists of a free-standing soft scaffold, skeletal muscle tissue, and optogenetic stem cell-derived neural cluster containing motor neurons. Myoblasts embedded in extracellular matrix self-organize into a muscle tissue guided by the geometry of the scaffold, and the resulting muscle tissue is cocultured in situ with a neural cluster. Motor neurons then extend neurites selectively toward the muscle and innervate it, developing functional neuromuscular units. Based on this initial construct, we computationally designed, optimized, and implemented light-sensitive flagellar swimmers actuated by these neuromuscular units. Cyclic muscle contractions, induced by neural stimulation, drive time-irreversible flagellar dynamics, thereby providing thrust for untethered forward locomotion of the swimmer. Overall, this work demonstrates an example of a biohybrid robot implementing neuromuscular actuation and illustrates a path toward the forward design and control of neuron-enabled biohybrid machines.

Modern inertial microfluidics routinely employs oscillatory flows around localized solid features or microbubbles for controlled, specific manipulation of particles, droplets, and cells. It is shown that theories of inertial effects that have been state of the art for decades miss major contributions and strongly underestimate forces on small suspended objects in a range of practically relevant conditions. An analytical approach is presented that derives a complete set of inertial forces and quantifies them in closed form as easy-to-use equations of motion, spanning the entire range from viscous to inviscid flows. The theory predicts additional attractive contributions toward oscillating boundaries, even for density-matched particles, a previously unexplained experimental observation. The accuracy of the theory is demonstrated against full-scale, three-dimensional direct numerical simulations throughout its range.

Disordered packings of unbonded, semiflexible fibers represent a class of materials spanning contexts and scales. From twig-based bird nests to unwoven textiles, bulk mechanics of disparate systems emerge from the bending of constituent slender elements about impermanent contacts. In experimental and computational packings of wooden sticks, we identify prominent features of their response to cyclic oedometric compression: non-linear stiffness, transient plasticity, and eventually repeatable velocity-independent hysteresis. We trace these features to their micromechanic origins, identified in characteristic appearance, disappearance, and displacement of internal contacts.

In this paper, we use the optimal control methodology to control a flexible, elastic Cosserat rod. An inspiration comes from stereotypical movement patterns in octopus arms, which are observed in a variety of manipulation tasks, such as reaching or fetching. To help uncover the mechanisms underlying these observed morphologies, we outline an optimal control-based framework. A single octopus arm is modeled as a Hamiltonian control system, where the continuum mechanics of the arm is modeled after the Cosserat rod theory, and internal, distributed muscle forces and couples are considered as controls. First order necessary optimality conditions are derived for an optimal control problem formulated for this infinite dimensional system. Solutions to this problem are obtained numerically by an iterative forward-backward algorithm. The state and adjoint equations are solved in a dynamic simulation environment, setting the stage for studying a broader class of optimal control problems. Trajectories that minimize control effort are demonstrated and qualitatively compared with experimentally observed behaviors.

The intriguing opportunities enabled by the use of living components in biological machines have spurred the development of a variety of muscle-powered bio-hybrid robots in recent years. Among them, several generations of bio-hybrid walkers have been established as reliable platforms to study untethered locomotion. However, despite these advances, such technology is not mature yet, and major challenges remain. This study takes steps to address two of them: the lack of systematic design approaches, common to bio-hybrid robotics in general, and in the case of bio-hybrid walkers specifically, the lack of maneuverability. We then present here a dual-ring biobot, computationally designed and selected to exhibit robust forward motion and rotational steering. This dual-ring biobot consists of two independent muscle actuators and a 4-legged scaffold asymmetric in the fore/aft direction. The integration of multiple muscles within its body architecture, combined with differential electrical stimulation, allows the robot to maneuver. The dual-ring robot design is then fabricated and experimentally tested, confirming computational predictions and turning abilities. Overall, our design approach based on modeling, simulation, and fabrication exemplified in this robot represents a route to efficiently engineer biological machines with adaptive functionalities.

Viscous streaming flows generated by objects of constant curvature (circular cylinders, infinite plates) have been well understood. Yet, characterization and understanding of such flows when multiple body length scales are involved has not been looked into in rigorous detail. We propose a simplified setting to understand and explore the effect of multiple body curvatures on streaming flows, analysing the system through the lens of bifurcation theory. Our set-up consists of periodic, regular lattices of cylinders characterized by two distinct radii, so as to inject discrete curvatures into the system, which in turn affect the streaming field generated due to an oscillatory background flow. We demonstrate that our understanding based on this system, and in particular the role of bifurcations in determining the local flow topology, can be then generalized to a variety of individual convex shapes presenting a spectrum of curvatures, explaining prior experimental and computational observations. Thus, this study illustrates a route towards the rational manipulation of viscous streaming flow topology, through regulated variation of object geometry.