@article {70, title = {Flutter instability in solids and structures, with a view on biomechanics and metamaterials}, journal = {Proceedings of the Royal Society A}, volume = {479}, year = {2023}, pages = {20230523}, abstract = {

The phenomenon of oscillatory instability called "flutter" was observed in aeroelasticity and rotor dynamics about a century ago. Driven by a series of applications involving non-conservative elasticity theory at different physical scales, ranging from nanomechanics to the mechanics of large space structures and including biomechanical problems of motility and growth, research on flutter is experiencing a new renaissance. A review is presented of the most notable applications and recent advances in fundamentals, both theoretical and experimental aspects, of flutter instability and Hopf bifurcation. Open problems, research gaps and new perspectives for investigations are indicated\ 

}, keywords = {elasticity, Hopf bifurcation, non-conservative systems, non-Hermitian mechanics, non-holonomic constraints}, doi = {10.1098/rspa.2023.0523}, author = {Davide Bigoni and Francesco Dal Corso and Oleg N. Kirillov and Diego Misseroni and Giovanni Noselli and Andrea Piccolroaz} } @article {69, title = {Nonreciprocal oscillations of polyelectrolyte gel filaments subject to a steady and uniform electric field}, journal = {Journal of the Mechanics and Physics of Solids}, volume = {173}, year = {2023}, pages = {105225}, abstract = {

Soft actuators typically require time-varying or spatially modulated control to be operationally effective. The scope of the present paper is to show, theoretically and experimentally, that a natural way to overcome this limitation is to exploit mechanical instabilities. We report experiments on active filaments of polyelectrolyte (PE) gels subject to a steady and uniform electric field. A large enough intensity of the field initiates the motion of the active filaments, leading to periodic oscillations. We develop a mathematical model based on morphoelasticity theory for PE gel filaments beating in a viscous fluid, and carry out the stability analysis of the governing equations to show the emergence of flutter and divergence instabilities for suitable values of the system{\textquoteright}s parameters. We confirm the results of the stability analysis with numerical simulations for the nonlinear equations of motion to show that such instabilities may lead to periodic self-sustained oscillations, in agreement with experiments. The key mechanism that underlies such behaviour is the capability of the filament to undergo active shape changes depending on its local orientation relative to the external electric field, in striking similarity with gravitropism, the mechanism that drives shape changes in plants via differential growth induced by gravity. Interestingly, the resulting oscillations are nonreciprocal in nature, and hence able to generate thrust and directed flow at low Reynolds number. The exploitation of mechanical instabilities in soft actuators represents a new avenue for the advancement in engineering design in fields such as micro-robotics and micro-fluidics.\ 

}, keywords = {Artificial cilia, Flutter and divergence instability, Polyelectrolyte gels, Self-sustained oscillations}, doi = {10.1016/j.jmps.2023.105225}, author = {Giancarlo Cicconofri and Valentina Damioli and Giovanni Noselli} } @article {67, title = {Transient shape morphing of active gel plates: Geometry and physics}, journal = {Soft Matter}, volume = {18}, year = {2022}, pages = {5867-5876}, chapter = {5867}, abstract = {

The control of shape in active structures is a key problem for the realization of smart sensors and actuators, which often draw inspiration from natural systems. In this context, slender structures, such as thin plates, have been studied as a relevant example of shape morphing systems where curvature is generated by in-plane incompatibilities. In particular, in hydrogel plates these incompatibilities can be programmed at fabrication time, such that a target configuration is attained at equilibrium upon swelling or shrinking. While these aspects have been examined in detail, understanding the transient morphing of such active structures deserves further investigation. In this study, we develop a geometrical model for the transient shaping of thin hydrogel plates by extending the theory of non-Euclidean plates. We validate the proposed model using experiments on gel samples that are programmed to reach axisymmetric equilibrium shapes. Interestingly, our experiments show the emergence of non-axisymmetric shapes for early times, as a consequence of boundary layer effects induced by solvent transport. We rationalize these observations using numerical simulations based on a detailed poroelastic model. Overall, this work highlights the limitations of purely geometrical models and the importance of transient, reduced theories for morphing plates that account for the coupled physics driving the evolution of shape. Computational approaches employing these theories will allow to achieve accurate control on the morphing dynamics and ultimately advance 4D printing technologies.\ 

}, keywords = {active materials, hydrogel plates, Transient morphing}, doi = {10.1039/D2SM00669C}, author = {Valentina Damioli and Erik Zorzin and Antonio DeSimone and Giovanni Noselli and Alessandro Lucantonio} } @article {65, title = {The biomechanical role of extra-axonemal structures in shaping the flagellar beat of Euglena gracilis}, journal = {eLife}, volume = {10:e58610}, year = {2021}, abstract = {

We propose and discuss a model for flagellar mechanics in Euglena gracilis. We show that the peculiar non-planar shapes of its beating flagellum, dubbed {\textquoteright}spinning lasso{\textquoteright}, arise from the mechanical interactions between two of its inner components, namely, the axoneme and the paraflagellar rod. The spontaneous shape of the axoneme and the resting shape of the paraflagellar rod are incompatible. Thus, the complex non-planar configurations of the coupled system emerge as the energetically optimal compromise between the two antagonistic components. The model is able to reproduce the experimentally observed flagellar beats and the characteristic geometric signature of spinning lasso, namely, traveling waves of torsion with alternating sign along the length of the flagellum.\ 

}, keywords = {Euglena gracilis, extra-axonemal structures, flagellar beat, flagellar mechanics, physics of living systems}, doi = {10.7554/eLife.58610}, author = {Giancarlo Cicconofri and Giovanni Noselli and Antonio De Simone} } @article {62, title = {How Euglena gracilis swims: Flow field reconstruction and analysis.}, journal = {Physical Review E}, volume = {103}, year = {2021}, pages = {023102}, abstract = {

Euglena gracilis is a unicellular organism that swims by beating a single anterior flagellum. We study the nonplanar waveforms spanned by the flagellum during a swimming stroke and the three-dimensional flows that they generate in the surrounding fluid. Starting from a small set of time-indexed images obtained by optical microscopy on a swimming Euglena cell, we construct a numerical interpolation of the stroke. We define an optimal interpolation (which we call synthetic stroke) by minimizing the discrepancy between experimentally measured velocities (of the swimmer) and those computed by solving numerically the equations of motion of the swimmer driven by the trial interpolated stroke. The good match we obtain between experimentally measured and numerically computed trajectories provides a first validation of our synthetic stroke. We further validate the procedure by studying the flow velocities induced in the surrounding fluid. We compare the experimentally measured flow fields with the corresponding quantities computed by solving numerically the Stokes equations for the fluid flow, in which the forcing is provided by the synthetic stroke, and find good matching. Finally, we use the synthetic stroke to derive a coarse-grained model of the flow field resolved in terms of a few dominant singularities. The far field is well approximated by a time-varying Stresslet, and we show that the average behavior of Euglena during one stroke is that of an off-axis puller. The reconstruction of the flow field closer to the swimmer body requires a more complex system of singularities. A system of two Stokeslets and one Rotlet, that can be loosely associated with the force exerted by the flagellum, the drag of the body, and a torque to guarantee rotational equilibrium, provides a good approximation.\ 

}, keywords = {BEM, flow reconstruction, general defocusing particle tracking, Micro-swimmers, non-planar flagellar wave forms, particle tracking velocimetry, Stokes singularities}, doi = {10.1103/PhysRevE.103.023102}, author = {Nicola Giuliani and Massimiliano Rossi and Giovanni Noselli and Antonio DeSimone} } @article {66, title = {Nutations in growing plant shoots as a morphoelastic flutter instability}, journal = {Philosophical Transactions of the Royal Society A}, volume = {379}, year = {2021}, pages = {20200116}, abstract = {

Recently, they have received renewed attention for the design and optimal actuation of bioinspired robotic devices. We discuss a possible interpretation of these spontaneous oscillations as a Hopf-type bifurcation in a growing morphoelastic rod. Using a three-dimensional model and numerical simulations, we analyse the salient features of this flutter-like phenomenon (e.g. the characteristic period of the oscillations) and their dependence on the model details (in particular, the impact of choosing different growth models) finding that, overall, these features are robust with respect to changes in the details of the growth model adopted.\ 

}, keywords = {circumutations, Gravitropism, Hopf bifurcation, morphoelastic rods}, doi = {doi.org/10.6084/m9.figshare.c.5354189}, author = {Daniele Agostinelli and Giovanni Noselli and Antonio De Simone} } @article {64, title = {Nutations in plant shoots: Endogenous and exogenous factors in the presence of mechanical deformations}, journal = {Frontiers in Plant Science - Plant Biophysics and Modeling}, volume = {12}, year = {2021}, pages = {371}, abstract = {

We present a three-dimensional morphoelastic rod model capable to describe the morphogenesis of growing plant shoots driven by differential growth. We discuss the evolution laws for endogenous oscillators, straightening mechanisms and reorientations to directional cues, such as gravitropic reactions governed by the avalanche dynamics of statoliths. We use this model to investigate the role of elastic deflections due to gravity loading in circumnutating plant shoots. We show that, in the absence of endogenous cues, pendular and circular oscillations arise as a critical length is attained, thus suggesting the occurrence of an instability triggered by exogenous factors. When also oscillations due to endogenous cues are present, their weight relative to those associated with the instability varies in time as the shoot length and other biomechanical properties change. Thanks to the simultaneous occurrence of these two oscillatory mechanisms, we are able to reproduce a variety of complex behaviors, including trochoid-like patterns, which evolve into circular orbits as the shoot length increases, and the amplitude of the exogenous oscillations becomes dominant.

}, keywords = {3d morphoelastic rods, circumnutation, Differential growth, plant morphogenesis, two-oscillator hypothesis}, doi = {10.3389/fpls.2021.608005}, author = {Daniele Agostinelli and Antonio DeSimone and Giovanni Noselli} } @article {63, title = {Rods coiling about a rigid constraint: Helices and perversions}, journal = {Proceedings of the Royal Society A}, volume = {477}, year = {2021}, pages = {20200817}, abstract = {

Mechanical instabilities can be exploited to design innovative structures, able to change their shape in the presence of external stimuli. In this work, we derive a mathematical model of an elastic beam subjected to an axial force and constrained to smoothly slide along a rigid support, where the distance between the rod midline and the constraint is fixed and finite. Using both theoretical and computational techniques, we characterize the bifurcations of such a mechanical system, in which the axial force and the natural curvature of the beam are used as control parameters. We show that, in the presence of a straight support, the rod can deform into shapes exhibiting helices and perversions, namely transition zones connecting together two helices with opposite chirality. The mathematical predictions of the proposed model are also compared with some experiments, showing a good quantitative agreement. In particular, we find that the buckled configurations may exhibit multiple perversions and we propose a possible explanation for this phenomenon based on the energy landscape of the mechanical system.

}, keywords = {bifurcation theory, elastic rods, finite-element simulations, helices, perversions, weakly nonlinear analysis}, doi = {/10.1098/rspa.2020.0817}, author = {Davide Riccobelli and Giovanni Noselli and Antonio DeSimone} } @article {59, title = {Mechanics of axisymmetric sheets of interlocking and slidable rods}, journal = {Journal of the Mechanics and Physics of Solids}, volume = {141}, year = {2020}, pages = {103969}, abstract = {

In this work, we study the mechanics of metamaterial sheets inspired by the pellicle of Euglenids. They are composed of interlocking elastic rods which can freely slide along their edges. We characterize the kinematics and the mechanics of these structures using the special Cosserat theory of rods and by assuming axisymmetric deformations of the tubular assembly. Through an asymptotic expansion, we investigate both structures that comprise a discrete number of rods and the limit case of a sheet composed by infinitely many rods. We apply our theoretical framework to investigate the stability of these structures in the presence of an axial load. Through a linear analysis, we compute the critical buckling force for both the discrete and the continuous case. For the latter, we also perform a numerical post-buckling analysis, studying the non-linear evolution of the bifurcation through finite elements simulations.\ 

}, keywords = {Biomimetic structures, Elastic structures, Helical rods, Mechanical instabilities, Metamaterials, Post-buckling analysis}, doi = {10.1016/j.jmps.2020.103969}, author = {Davide Riccobelli and Giovanni Noselli and Marino Arroyo and Antonio De Simone} } @article {57, title = {Morphable structures from unicellular organisms with active, shape-shifting envelopes: Variations on a theme by Gauss}, journal = {International Journal of Non{\textendash}Linear Mechanics}, volume = {118}, year = {2020}, pages = {103278}, abstract = {

We discuss some recent results on biological and bio-inspired morphing, and use them to identify promising research directions for the future. In particular, we consider issues related to morphing at microscopic scales inspired by unicellular organisms. We focus on broad conceptual principles and, in particular, on morphing approaches based on the use of Gauss{\textquoteright} theorema egregium (Gaussian morphing). We highlight some connections with biological cell envelopes containing filaments and motors, and discuss ideas for the implementation of Gaussian morphing in surfaces actuated by active shearing or stretching.\ 

}, keywords = {Active shells, cell motility, Deployable structures, Fluid{\textendash}structure interaction, Gaussian morphing, Micro-swimmers, soft robotics, Unicellular swimmers}, doi = {10.1016/j.ijnonlinmec.2019.103278}, author = {Giancarlo Cicconofri and Giovanni Noselli and Marino Arroyo and Antonio De Simone} } @article {56, title = {Nutations in growing plant shoots: The role of elastic deformations due to gravity loading}, journal = {Journal of the Mechanics and Physics of Solids}, volume = {136}, year = {2020}, pages = {103702}, abstract = {

The effect of elastic deformations induced by gravity loading on the active circumnutation movements of growing plant shoots is investigated. We consider first a discrete model (a gravitropic spring-pendulum system) and then a continuous rod model which is analyzed both analytically (under the assumption of small deformations) and numerically (in the large deformation regime). We find that, for a choice of material parameters consistent with values reported in the available literature on plant shoots, rods of sufficient length may exhibit lateral oscillations of increasing amplitude, which eventually converge to limit cycles. This behavior strongly suggests the occurrence of a Hopf bifurcation, just as for the gravitropic spring-pendulum system, for which this result is rigorously established. At least in this restricted set of material parameters, our analysis supports a view of Darwin{\textquoteright}s circumnutations as a biological analogue to structural systems exhibiting flutter instabilities, i.e., spontaneous oscillations away from equilibrium configurations driven by non-conservative loads. Here, in the context of nutation movements of growing plant shoots, the energy needed to sustain oscillations is continuously supplied to the system by the internal biochemical machinery presiding the capability of plants to maintain a vertical pose.\ 

}, keywords = {Circumnutations, Flutter instability, Gravitropism, Hopf bifurcation}, doi = {10.1016/j.jmps.2019.103702}, author = {Agostinelli, Daniele and Lucantonio, Alessandro and Noselli, Giovanni and DeSimone, Antonio} } @article {58, title = {On polymer network rupture in gels in the limit of very slow straining or a very slow crack propagation rate}, journal = {Journal of the Mechanics and Physics of Solids}, volume = {136}, year = {2020}, pages = {103754}, abstract = {

The J-integral is formulated in a direct manner for a gel consisting of a cross-linked polymer network and a mobile solvent. The form of the J-integral is given for a formulation that exploits the Helmholtz energy density of the gel and expressions are provided for it in both the unswollen reference configuration of the polymer network and in the current swollen configuration of the gel when small strains are superimposed on the swollen state. Similarly, the form of the J-integral is developed for an approach that exploits the Landau energy density of the gel and its reference and current configuration expressions are also developed. The Flory-Rehner model of the gel is used to obtain expressions for both the densities of Helmholtz energy and the Landau energy, with the chemical potential of the solvent derived from the Helmholtz energy used in the Legendre transformation that generates the Landau energy. Both the Helmholtz and Landau energies are expanded asymptotically for small strains superimposed on the swollen state of the gel. The results for the various forms of the energies are then used to obtain the elasticity law and the incompressibility constraint for the gel, each derived from both the Helmholtz and the Landau energies. The results are then inserted into the J-integral and fracture mechanics insights obtained for the rapid and slow loading of a gel body with a stationary crack and for a gel body with a crack that is experiencing slow, steady propagation. It is found that the Landau energy form of the J-integral is particularly useful for the slow loading of stationary cracks and for the slow steady propagation of the crack. It is noted that solvent flux during crack growth can cause an increase in the effective fracture toughness of the gel. However, it is found that there is an absence of such diffusional toughening in the rapidly loaded stationary crack case, the very slowly loaded stationary crack case and for the crack experiencing extremely slow but steady propagation. It is further found that, for cracks propagating very slowly, diffusional toughening rises linearly with crack propagation rate up to a critical crack growth rate, above which the diffusional toughening becomes insensitive to the crack propagation rate. The critical crack propagation rate for this transition is found to be dependent on the linear dimension of the gel body and on constitutive parameters for the gel elasticity and solvent diffusion.\ 

}, keywords = {J-integral, polymer gel, Rupture, Slow crack growth, Toughness}, doi = {10.1016/j.jmps.2019.103754}, author = {Robert M McMeeking and Alessandro Lucantonio and Giovanni Noselli and Vikram S Deshpande} } @article {54, title = {Smart helical structures inspired by the pellicle of euglenids}, journal = {Journal of the Mechanics and Physics of Solids}, volume = {123}, year = {2019}, pages = {234-246}, abstract = {

This paper deals with a concept for a reconfigurable structure bio-inspired by the cell wall architecture of euglenids, a family of unicellular protists, and based on the relative sliding of adjacent strips. Uniform sliding turns a cylinder resulting from the assembly of straight and parallel strips into a cylinder of smaller height and larger radius, in which the strips are deformed into a family of parallel helices. We examine the mechanics of this cylindrical assembly, in which the interlocking strips are allowed to slide freely at their junctions, and compute the external forces (axial force and axial torque at the two ends, or pressure on the lateral surface) necessary to drive and control the shape changes of the composite structure. Despite the simplicity of the structure, we find a remarkably complex mechanical behaviour that can be tuned by the spontaneous curvature or twist of the strips.\ 

}, keywords = {Bio-inspired structures, Euglenoid pellicle, Helical bundles, Morphing structures, Reconfigurable structures}, doi = {10.1016/j.jmps.2018.09.036}, author = {Noselli, Giovanni and Arroyo, Marino and DeSimone, Antonio} } @article {55, title = {Swimming Euglena respond to confinement with a behavioural change enabling effective crawling}, journal = {Nature Physics}, volume = {15}, year = {2019}, pages = {496-502}, abstract = {

Some euglenids, a family of aquatic unicellular organisms, can develop highly concerted, large-amplitude peristaltic body deformations. This remarkable behaviour has been known for centuries. Yet, its function remains controversial, and is even viewed as a functionless ancestral vestige. Here, by examining swimming Euglena\ gracilis in environments of controlled crowding and geometry, we show that this behaviour is triggered by confinement. Under these conditions, it allows cells to switch from unviable flagellar swimming to a new and highly robust mode of fast crawling, which can deal with extreme geometric confinement and turn both frictional and hydraulic resistance into propulsive forces. To understand how a single cell can control such an adaptable and robust mode of locomotion, we developed a computational model of the motile apparatus of Euglena cells consisting of an active striated cell envelope. Our modelling shows that gait adaptability does not require specific mechanosensitive feedback but instead can be explained by the mechanical self-regulation of an elastic and extended motor system. Our study thus identifies a locomotory function and the operating principles of the adaptable peristaltic body deformation of Euglena cells.

}, keywords = {crawling motility, Euglena gracilis, Metaboly, Spatial confinement}, doi = {10.1038/s41567-019-0425-8}, author = {Noselli, Giovanni and Beran, Alfred and Arroyo, Marino and DeSimone, Antonio} } @article {53, title = {A fluorescent dye method suitable for visualization of one or more rat whiskers}, journal = {Bio-protocol}, volume = {8}, year = {2018}, chapter = {e2749}, abstract = {

Visualization and tracking of the facial whiskers is critical to many studies of rodent behavior. High-speed videography is the most robust methodology for characterizing whisker kinematics, but whisker visualization is challenging due to the low contrast of the whisker against its background. Recently, we showed that fluorescent dye(s) can be applied to enhance visualization and tracking of whisker(s) (Rigosa et al., 2017), and this protocol provides additional details on the technique.\ 

}, keywords = {barrel cortex, Dye, Fluorescence, Tactile perception, Tracking, Whisker}, doi = {10.21769/BioProtoc.2749}, author = {Jacopo Rigosa and Alessandro Lucantonio and Giovanni Noselli and Arash Fassihi and Fabrizio Manzino and Francesca Pulecchi and Mathew E Diamond} } @article {44, title = {Dye-enhanced visualization of rat whiskers for behavioral studies}, journal = {eLife}, volume = {6:e25290}, year = {2017}, abstract = {

Visualization and tracking of the facial whiskers is required in an increasing number of rodent studies. Though many approaches have been employed, only high-speed videography has proven adequate for measuring whisker motion and deformation during interaction with an object. However, whisker visualization and tracking is challenging for multiple reasons, primary among them the low contrast of the whisker against its background. Here we demonstrate a fluorescent dye method suitable for visualization of one or more rat whiskers. The process makes the dyed whisker(s) easily visible against a dark background. The coloring does not influence the behavioral performance of rats trained on a vibrissal vibrotactile discrimination task, nor does it affect the whiskers{\textquoteright} mechanical properties.

}, keywords = {behavioral studies, dye-enhanced visualization, rat whiskers}, doi = {10.7554/eLife.25290}, author = {Jacopo Rigosa and Alessandro Lucantonio and Giovanni Noselli and Arash Fassihi and Erik Zorzin and Fabrizio Manzino and Francesca Pulecchi and Mathew E Diamond} } @article {52, title = {Kinematics of flagellar swimming in Euglena gracilis: Helical trajectories and flagellar shapes}, journal = {Proceedings of the National Academy of Sciences of USA}, volume = {114}, year = {2017}, pages = {13085{\textendash}13090}, abstract = {

The flagellar swimming of euglenids, which are propelled by a single anterior flagellum, is characterized by a generalized helical motion. The 3D nature of this swimming motion, which lacks some of the symmetries enjoyed by more common model systems, and the complex flagellar beating shapes that power it make its quantitative description challenging. In this work, we provide a quantitative, 3D, highly resolved reconstruction of the swimming trajectories and flagellar shapes of specimens of Euglena gracilis. We achieved this task by using high-speed 2D image recordings taken with a conventional inverted microscope combined with a precise characterization of the helical motion of the cell body to lift the 2D data to 3D trajectories. The propulsion mechanism is discussed. Our results constitute a basis for future biophysical research on a relatively unexplored type of eukaryotic flagellar movement.\ 

}, keywords = {3D flagellum shapes, Euglena gracilis, helical trajectories, microscopy imaging, microswimmers}, doi = {10.1073/pnas.1708064114}, author = {Massimiliano Rossi and Giancarlo Cicconofri and Alfred Beran and Giovanni Noselli and Antonio DeSimone} } @article {46, title = {Large-strain poroelastic plate theory for polymer gels with applications to swelling-induced morphing of composite plates}, journal = {Composites Part B: Engineering}, volume = {115}, year = {2017}, pages = {330-340}, abstract = {

We derive a large-strain plate model that allows to describe transient, coupled processes involving elasticity and solvent migration, by performing a dimensional reduction of a three-dimensional poroelastic theory. We apply the model to polymer gel plates, for which a specific kinematic constraint and constitutive relations hold. Finally, we assess the accuracy of the plate model with respect to the parent three-dimensional model through two numerical benchmarks, solved by means of the finite element method. Our results show that the theory offers an efficient computational framework for the study of swelling-induced morphing of composite gel plates.

}, keywords = {large strain, plates, polymer gel, swelling}, doi = {10.1016/j.compositesb.2016.09.063}, author = {Alessandro Lucantonio and Giuseppe Tomassetti and Antonio DeSimone} } @article {51, title = {Spontaneous morphing of equibiaxially pre-stretched elastic bilayers: the role of sample geometry}, journal = {International Journal of Mechanical Sciences}, volume = {In press.}, year = {2017}, abstract = {

An elastic bilayer, consisting of an equibiaxially pre-stretched sheet bonded to a stress-free one, spontaneously morphs into curved shapes in the absence of external loads or constraints. Using experiments and numerical simulations, we explore the role of geometry for square and rectangular samples in determining the equilibrium shape of the system, for a fixed pre-stretch. We classify the observed shapes over a wide range of aspect ratios according to their curvatures and compare measured and computed values, which show good agreement. In particular, as the bilayer becomes thinner, a bifurcation of the principal curvatures occurs, which separates two scaling regimes for the energy of the system. We characterize the transition between these two regimes and show the peculiar features that distinguish square from rectangular samples. The results for our model bilayer system may help explaining morphing in more complex systems made of active materials.\ 

}, keywords = {Bifurcation, Elastic bilayer, Pre-stretch, Shape programming}, doi = {10.1016/j.ijmecsci.2017.08.049}, author = {No{\`e} Caruso and Aleksandar Cvetkovi{\'c} and Alessandro Lucantonio and Giovanni Noselli and Antonio DeSimone} } @article {45, title = {Continuum theory of swelling material surfaces with applications to thermo-responsive gel membranes and surface mass transport}, journal = {Journal of the Mechanics and Physics of Solids}, volume = {89}, year = {2016}, pages = {96-109}, abstract = {

Soft membranes are commonly employed in shape-morphing applications, where the material is programmed to achieve a target shape upon activation by an external trigger, and as coating layers that alter the surface characteristics of bulk materials, such as the properties of spreading and absorption of liquids. In particular, polymer gel membranes experience swelling or shrinking when their solvent content change, and the non-homogeneous swelling field may be exploited to control their shape. Here, we develop a theory of swelling material surfaces to model polymer gel membranes and demonstrate its features by numerically studying applications in the contexts of biomedicine, micro-motility, and coating technology. We also specialize the theory to thermo-responsive gels, which are made of polymers that change their affinity with a solvent when temperature varies.

}, keywords = {drug delivery, material surface, membrane, micro-motility, polymer gel, spreading, swelling}, doi = {10.1016/j.jmps.2016.02.001}, author = {Alessandro Lucantonio and Luciano Teresi and Antonio DeSimone} } @article {49, title = {Motion planning and motility maps for flagellar microswimmers}, journal = {The European Physical Journal E}, volume = {39}, year = {2016}, pages = {72-86}, abstract = {

We study two microswimmers consisting of a spherical rigid head and a passive elastic tail. In the first one the tail is clamped to the head, and the system oscillates under the action of an external torque. In the second one, head and tail are connected by a joint allowing the angle between them to vary periodically, as a result of an oscillating internal torque. Previous studies on these models were restricted to sinusoidal actuations, showing that the swimmers can propel while moving on average along a straight line, in the direction given by the symmetry axis around which beating takes place. We extend these results to motions produced by generic (non-sinusoidal) periodic actuations within the regime of small compliance of the tail. We find that modulation in the velocity of actuation can provide a mechanism to select different directions of motion. With velocity-modulated inputs, the externally actuated swimmer can translate laterally with respect to the symmetry axis of beating, while the internally actuated one is able to move along curved trajectories. The governing equations are analysed with an asymptotic perturbation scheme, providing explicit formulas, whose results are expressed through motility maps. Asymptotic approximations are further validated by numerical simulations.

}, keywords = {flagellar motility, microswimmers, motion planning}, doi = {10.1140/epje/i2016-16072-y}, author = {Giancarlo Cicconofri and Antonio DeSimone} } @article {41, title = {Poroelastic toughening in polymer gels: A theoretical and numerical study}, journal = {Journal of the Mechanics and Physics of Solids}, volume = {94}, year = {2016}, pages = {33-46}, abstract = {

We explore the Mode I fracture toughness of a polymer gel containing a semi-infinite, growing crack. First, an expression is derived for the energy release rate within the linearized, small-strain setting. This expression reveals a crack tip velocity-independent toughening that stems from the poroelastic nature of polymer gels. Then, we establish a poroelastic cohesive zone model that allows us to describe the micromechanics of fracture in gels by identifying the role of solvent pressure in promoting poroelastic toughening. We evaluate the enhancement in the effective fracture toughness through asymptotic analysis. We confirm our theoretical findings by means of numerical simulations concerning the case of a steadily propagating crack. In broad terms, our results explain the role of poroelasticity and of the processes occurring in the fracturing region in promoting toughening of polymer gels.

}, keywords = {crack propagation, fracture, polymer gel, swelling, toughening}, doi = {10.1016/j.jmps.2016.04.017}, author = {Giovanni Noselli and Alessandro Lucantonio and Robert M McMeeking and Antonio DeSimone} } @article {40, title = {Hydraulic fracture and toughening of a brittle layer bonded to a hydrogel}, journal = {Physical Review Letters}, volume = {115}, year = {2015}, pages = {188105}, abstract = {

Brittle materials propagate opening cracks under tension. When stress increases beyond a critical magnitude, then quasistatic crack propagation becomes unstable. In the presence of several precracks, a brittle material always propagates only the weakest crack, leading to catastrophic failure. Here, we show that all these features of brittle fracture are fundamentally modified when the material susceptible to cracking is bonded to a hydrogel, a common situation in biological tissues. In the presence of the hydrogel, the brittle material can fracture in compression and can hydraulically resist cracking in tension. Furthermore, the poroelastic coupling regularizes the crack dynamics and enhances material toughness by promoting multiple cracking.

}, keywords = {hydraulic fracture, multiple-cracking, toughening}, doi = {10.1103/PhysRevLett.115.188105}, author = {Alessandro Lucantonio and Giovanni Noselli and Xavier Trepat and Marino Arroyo and Antonio DeSimone} } @article {39, title = {Liquid crystal elastomer strips as soft crawlers}, journal = {Journal of the Mechanics and Physics of Solids}, volume = {84}, year = {2015}, pages = {254-272}, abstract = {

In this paper, we speculate on a possible application of Liquid Crystal Elastomers to the field of soft robotics. In particular, we study a concept for limbless locomotion that is amenable to miniaturisation. For this purpose, we formulate and solve the evolution equations for a strip of nematic elastomer, subject to directional frictional interactions with a flat solid substrate, and cyclically actuated by a spatially uniform, time-periodic stimulus (e.g., temperature change). The presence of frictional forces that are sensitive to the direction of sliding transforms reciprocal, {\textquoteleft}breathing-like{\textquoteright} deformations into directed forward motion. We derive formulas quantifying this motion in the case of distributed friction, by solving a differential inclusion for the displacement field. The simpler case of concentrated frictional interactions at the two ends of the strip is also solved, in order to provide a benchmark to compare the continuously distributed case with a finite-dimensional benchmark. We also provide explicit formulas for the axial force along the crawler body.

}, keywords = {crawling motility, directional surfaces, frictional interactions, liquid crystal elastomers, soft biomimetic robots}, doi = {10.1016/j.jmps.2015.07.017}, author = {Antonio DeSimone and Paolo Gidoni and Giovanni Noselli} } @article {47, title = {Motility of a model bristle-bot: A theoretical analysis}, journal = {International Journal of Non-Linear Mechanics}, volume = {76}, year = {2015}, pages = {233-239}, abstract = {

Bristle-bots are legged robots that can be easily made out of a toothbrush head and a small vibrating engine. Despite their simple appearance, the mechanism enabling them to propel themselves by exploiting friction with the substrate is far from trivial. Numerical experiments on a model bristle-bot have been able to reproduce such a mechanism revealing, in addition, the ability to switch direction of motion by varying the vibration frequency. This paper provides a detailed account of these phenomena through a fully analytical treatment of the model. The equations of motion are solved through an expansion in terms of a properly chosen small parameter. The convergence of the expansion is rigorously proven. In addition, the analysis delivers formulas for the average velocity of the robot and for the frequency at which the direction switch takes place. A quantitative description of the mechanism for the friction modulation underlying the motility of the bristle-bot is also provided.

}, keywords = {bristle-robots, crawling motility, frictional interactions}, doi = {10.1016/j.ijnonlinmec.2014.12.010}, author = {Giancarlo Cicconofri and Antonio DeSimone} } @article {48, title = {A study of snake-like locomotion through the analysis of a flexible robot model}, journal = {Proceedings of the Royal Society A}, volume = {471}, year = {2015}, pages = {20150054}, abstract = {

We examine the problem of snake-like locomotion by studying a system consisting of a planar inextensible elastic rod with adjustable spontaneous curvature, which provides an internal actuation mechanism that mimics muscular action in a snake. Using a Cosserat model, we derive the equations of motion in two special cases: one in which the rod can only move along a prescribed curve, and one in which the rod is constrained to slide longitudinally without slipping laterally, but the path is not fixed a priori (free-path case). The second setting is inspired by undulatory locomotion of snakes on flat surfaces. The presence of constraints leads in both cases to non-standard boundary conditions that allow us to close and solve the equations of motion. The kinematics and dynamics of the system can be recovered from a one-dimensional equation, without any restrictive assumption on the followed trajectory or the actuation. We derive explicit formulae highlighting the role of spontaneous curvature in providing the driving force (and the steering, in the free-path case) needed for locomotion. We also provide analytical solutions for a special class of serpentine motions, which enable us to discuss the connection between observed trajectories, internal actuation and forces exchanged with the environment.

}, keywords = {bioinspired robots, Cosserat rod models, limbless locomotion, snake locomotion, soft robotics, undulatory locomotion}, doi = {10.1098/rspa.2015.0054}, author = {Giancarlo Cicconofri and Antonio DeSimone} } @article {36, title = {Crawling on directional surfaces}, journal = {International Journal of Non-Linear Mechanics}, volume = {61}, year = {2014}, pages = {65-73}, abstract = {

In this paper we study crawling locomotion based on directional frictional interactions, namely, frictional forces that are sensitive to the sign of the sliding velocity. Surface interactions of this type are common in biology, where they arise from the presence of inclined hairs or scales at the crawler/substrate interface, leading to low resistance when sliding {\textquoteleft}along the grain{\textquoteright}, and high resistance when sliding {\textquoteleft}against the grain{\textquoteright}. This asymmetry can be exploited for locomotion, in a way analogous to what is done in cross-country skiing (classic style, diagonal stride). We focus on a model system, namely, a continuous one-dimensional crawler and provide a detailed study of the motion resulting from several strategies of shape change. In particular, we provide explicit formulae for the displacements attainable with reciprocal extensions and contractions (breathing), or through the propagation of extension or contraction waves. We believe that our results will prove particularly helpful for the study of biological crawling motility and for the design of bio-mimetic crawling robots.

}, keywords = {bio-mimetic micro-robots, cell migration, crawling motility, directional surfaces, self-propulsion}, doi = {10.1016/j.ijnonlinmec.2014.01.012}, author = {Paolo Gidoni and Giovanni Noselli and Antonio DeSimone} } @article {35, title = {Discrete one-dimensional crawlers on viscous substrates: achievable net displacements and their energy cost}, journal = {Mechanics Research Communications}, volume = {58}, year = {2014}, pages = {73{\textendash}81}, abstract = {

We study model one-dimensional crawlers, namely, model mechanical systems that can achieve self-propulsion by controlled shape changes of their body (extension or contraction of portions of the body), thanks to frictional interactions with a rigid substrate. We evaluate the achievable net displacement and the related energetic cost for self-propulsion by discrete crawlers (i.e., whose body is made of a discrete number of contractile or extensile segments) moving on substrates with either a Newtonian (linear) or a Bingham-type (stick-slip) rheology. Our analysis is aimed at constructing the basic building blocks towards an integrative, multi-scale description of crawling cell motility.

}, keywords = {cell migration, cell motility, crawling motility, limbless locomotion, motility on a solid substrate, self-propulsion, soft biomimetic robots}, doi = {10.1016/j.mechrescom.2013.10.023}, author = {Giovanni Noselli and Amabile Tatone and Antonio DeSimone} } @article {38, title = {A robotic crawler exploiting directional frictional interactions: Experiments, numerics and derivation of a reduced model}, journal = {Proceedings of the Royal Society A}, volume = {470}, year = {2014}, pages = {20140333}, abstract = {

We present experimental and numerical results for a model crawler which is able to extract net positional changes from reciprocal shape changes, i.e. {\textquoteleft}breathing-like{\textquoteright} deformations, thanks to directional, frictional interactions with a textured solid substrate, mediated by flexible inclined feet. We also present a simple reduced model that captures the essential features of the kinematics and energetics of the gait, and compare its predictions with the results from experiments and from numerical simulations.

}, keywords = {breathing-like deformations, crawling motility, directional interactions, directional surfaces, scallop theorem}, doi = {10.1098/rspa.2014.0333}, author = {Giovanni Noselli and Antonio DeSimone} } @article {37, title = {Shape control of active surfaces inspired by the movement of euglenids}, journal = {Journal of the Mechanics and Physics of Solids}, volume = {62}, year = {2014}, pages = {99-112}, abstract = {

We examine a novel mechanism for active surface morphing inspired by the cell body deformations of euglenids. Actuation is accomplished through in-plane simple shear along prescribed slip lines decorating the surface. Under general non-uniform actuation, such local deformation produces Gaussian curvature, and therefore leads to shape changes. Geometrically, a deformation that realizes the prescribed local shear is an isometric embedding. We explore the possibilities and limitations of this bio-inspired shape morphing mechanism, by first characterizing isometric embeddings under axisymmetry, understanding the limits of embeddability, and studying in detail the accessibility of surfaces of zero and constant curvature. Modeling mechanically the active surface as a non-Euclidean plate (NEP), we further examine the mechanism beyond the geometric singularities arising from embeddability, where mechanics and buckling play a decisive role. We also propose a non-axisymmetric actuation strategy to accomplish large amplitude bending and twisting motions of elongated cylindrical surfaces. Besides helping understand how euglenids delicately control their shape, our results may provide the background to engineer soft machines.

}, keywords = {active materials, cell motility, Euglenids, non-Euclidean plates}, doi = {10.1016/j.jmps.2013.09.017}, author = {Marino Arroyo and Antonio DeSimone} } @article {50, title = {An analysis of competing toughening mechanisms in layered and particulate solids}, journal = {International Journal of Fracture}, volume = {183}, year = {2013}, pages = {241-258}, abstract = {

The relative potency of common toughening mechanisms is explored for layered solids and particulate solids, with an emphasis on crack multiplication and plasticity. First, the enhancement in toughness due to a parallel array of cracks in an elastic solid is explored, and the stability of co-operative cracking is quantified. Second, the degree of synergistic toughening is determined for combined crack penetration and crack kinking at the tip of a macroscopic, mode I crack; specifically, the asymptotic problem of self-similar crack advance (penetration mode) versus 90{\textdegree} symmetric kinking is considered for an isotropic, homogeneous solid with weak interfaces. Each interface is treated as a cohesive zone of finite strength and toughness. Third, the degree of toughening associated with crack multiplication is assessed for a particulate solid comprising isotropic elastic grains of hexagonal shape, bonded by cohesive zones of finite strength and toughness. The study concludes with the prediction of R-curves for a mode I crack in a multi-layer stack of elastic and elastic{\textendash}plastic solids. A detailed comparison of the potency of the above mechanisms and their practical application are given. In broad terms, crack tip kinking can be highly potent, whereas multiple cracking is difficult to activate under quasi-static conditions. Plastic dissipation can give a significant toughening in multi-layers especially at the nanoscale.

}, keywords = {crack resistance curves, multi-layered composites, particulate solids, toughening mechanisms}, doi = {10.1007/s10704-013-9890-8}, author = {Giovanni Noselli and Vikram S Deshpande and Norman A Fleck} } @article {30, title = {Crawlers in viscous environments: linear vs. nonlinear rheologies}, journal = {International Journal of Non-Linear Mechanics}, volume = {56}, year = {2013}, pages = {142-147}, abstract = {

We study model self-propelled crawlers which derive their propulsive capabilities from the tangential resistance to motion offered by the environment. Two types of relationships between tangential force and slip velocity are considered: a linear, Newtonian one and a nonlinear one of Bingham-type. Different behaviors result from the two different rheologies. These differences and their implications in terms of motility performance are discussed. Our aim is to develop new tools and insight for future studies of cell motility by crawling.

}, keywords = {cell migration, cell motility, crawling motility, motility on a solid substrate, self-propulsion, soft biomimetic robots}, doi = {10.1016/j.ijnonlinmec.2013.02.007}, author = {Antonio DeSimone and Federica Guarnieri and Giovanni Noselli and Amabile Tatone} } @article {32, title = {Behavioral study of whisker-mediated vibration sensation in rats}, journal = {Proceedings of the National Academy of Sciences of USA}, volume = {109}, year = {2012}, pages = {971{\textendash}976}, abstract = {

Rats use their vibrissal sensory system to collect information about the nearby environment. They can accurately and rapidly identify object location, shape, and surface texture. Which features of whisker motion does the sensory system extract to construct sensations? We addressed this question by training rats to make discriminations between sinusoidal vibrations simultaneously presented to the left and right whiskers. One set of rats learned to reliably identify which of two vibrations had higher frequency (f1 vs. f2) when amplitudes were equal. Another set of rats learned to reliably identify which of two vibrations had higher amplitude (A1 vs. A2) when frequencies were equal. Although these results indicate that both elemental features contribute to the rats{\textquoteright} sensation, a further test found that the capacity to discriminate A and f was reduced to chance when the difference in one feature was counterbalanced by the difference in the other feature: Rats could not discriminate amplitude or frequency whenever A1f1 = A2f2. Thus, vibrations were sensed as the product Af rather than as separable elemental features, A and f. The product Af is proportional to a physical entity, the mean speed. Analysis of performance revealed that rats extracted more information about differences in Af than predicted by the sum of the information in elemental differences. These behavioral experiments support the predictions of earlier physiological studies by demonstrating that rats are {\textquotedblleft}blind{\textquotedblright} to the elemental features present in a sinusoidal whisker vibration; instead, they perceive a composite feature, the speed of whisker motion.

}, keywords = {barrel cortex, coding}, doi = {10.1073/pnas.1116726109}, author = {Mehdi Adibi and Mathew E. Diamond and Ehsan Arabzadeh} } @article {28, title = {Crawling motility through the analysis of model locomotors: two case studies}, journal = {The European Physical Journal E}, volume = {35}, year = {2012}, pages = {1-8}, abstract = {

We study model locomotors on a substrate, which derive their propulsive capabilities from the tangential (viscous or frictional) resistance offered by the substrate. Our aim is to develop new tools and insight for future studies of cellular motility by crawling and of collective bacterial motion. The purely viscous case (worm) is relevant for cellular motility by crawling of individual cells. We re-examine some recent results on snail locomotion in order to assess the role of finely regulated adhesion mechanisms in crawling motility. Our main conclusion is that such regulation, although well documented in several biological systems, is not indispensable to accomplish locomotion driven by internal deformations, provided that the crawler may execute sufficiently large body deformations. Thus, there is no snail theorem. Namely, the crawling analog of the scallop theorem of low Reynolds number hydrodynamics does not hold for snail-like crawlers. The frictional case is obtained by assuming that the viscous coefficient governing tangential resistance forces, which act parallel and in the direction opposite to the velocity of the point to which they are applied, depends on the normal force acting at that point. We combine these surface interactions with inertial effects in order to investigate the mechanisms governing the motility of a bristle-robot. This model locomotor is easily manufactured and has been proposed as an effective tool to replicate and study collective bacterial motility.

}, keywords = {crawling motility}, doi = {10.1140/epje/i2012-12085-x}, author = {Antonio DeSimone and Amabile Tatone} } @article {31, title = {Reverse engineering the euglenoid movement}, journal = {Proceedings of the National Academy of Sciences of USA}, volume = {109}, year = {2012}, pages = {17874{\textendash}17879}, abstract = {

Euglenids exhibit an unconventional motility strategy amongst unicellular eukaryotes, consisting of large-amplitude highly concerted deformations of the entire body (euglenoid movement or metaboly). A plastic cell envelope called pellicle mediates these deformations. Unlike ciliary or flagellar motility, the biophysics of this mode is not well understood, including its efficiency and molecular machinery. We quantitatively examine video recordings of four euglenids executing such motions with statistical learning methods. This analysis reveals strokes of high uniformity in shape and pace. We then interpret the observations in the light of a theory for the pellicle kinematics, providing a precise understanding of the link between local actuation by pellicle shear and shape control. We systematically understand common observations, such as the helical conformations of the pellicle, and identify previously unnoticed features of metaboly. While two of our euglenids execute their stroke at constant body volume, the other two exhibit deviations of about 20\% from their average volume, challenging current models of low Reynolds number locomotion. We find that the active pellicle shear deformations causing shape changes can reach 340\%, and estimate the velocity of the molecular motors. Moreover, we find that metaboly accomplishes locomotion at hydrodynamic efficiencies comparable to those of ciliates and flagellates. Our results suggest new quantitative experiments, provide insight into the evolutionary history of euglenids, and suggest that the pellicle may serve as a model for engineered active surfaces with applications in microfluidics.

}, keywords = {active soft matter, microswimmers, self-propulsion, stroke kinematics}, doi = {10.1073/pnas.1213977109}, author = {Marino Arroyo and Luca Heltai and Daniel Mill{\'a}n and Antonio DeSimone} } @article {34, title = {Unsupervised quantification of whisking and head movement in freely moving rodents}, journal = {Journal of Neurophysiology}, volume = {105}, year = {2011}, pages = {1950-1962}, abstract = {

The rodent whisker system has become the leading experimental paradigm for the study of active sensing. Thanks to more sophisticated behavioral paradigms, progressively better neurophysiological methods, and improved video hardware/software, there is now the prospect of defining the precise connection between the sensory apparatus and brain activity in awake, exploring animals. Achieving this ambitious goal requires quantitative, objective characterization of head and whisker kinematics. This study presents the methodology and potential uses of a new automated motion analysis routine. The program provides full quantification of head orientation and translation, as well as the angle, frequency, amplitude, and bilateral symmetry of whisking. The system operates without any need for manual tracing by the user. Quantitative comparison to whisker detection by expert humans indicates that the program{\textquoteright}s correct detection rate is at \>95\% even on animals with all whiskers intact. Particular attention has been paid to obtaining reliable performance under nonoptimal lighting or video conditions and at frame rates as low as 100. Variation of the zoom across time is compensated for without user intervention. The program adapts automatically to the size and shape of different species. The outcome of our testing indicates that the program can be a valuable tool in quantifying rodent sensorimotor behavior.

}, keywords = {head tracking, snout tracking, whisker tracking}, doi = {10.1152/jn.00764.2010}, author = {Igor Perkon and Andrej Kosir and Pavel M Itskov and Jurij Tasic and Mathew E. Diamond} } @article {33, title = {Whisking and whisker kinematics during a texture classification task}, journal = {Philosophical Transactions of the Royal Society B}, volume = {366}, year = {2011}, pages = {3058-3069}, abstract = {

Rats explore objects by rhythmically whisking with their vibrissae. The goal of the present study is to learn more about the motor output used by rats to acquire texture information as well as the whisker motion evoked by texture contact. We trained four rats to discriminate between different grooved textures and used high-speed video to characterize whisker motion during the task. The variance in whisking parameters among subjects was notable. After whisker trimming, the animals changed their behaviour in ways that appear consistent with an optimization of whisker movement to compensate for lost information. These results lead to the intriguing notion that the rats use an information-seeking {\textquoteleft}cognitive{\textquoteright} motor strategy, instead of a rigid motor programme. Distinct stick/slip events occurred during texture palpation and their frequency increased in relation to the spatial frequency of the grooves. The results allow a preliminary assessment of three candidate texture-coding mechanisms{\textemdash}the number of grooves encountered during each touch, the temporal difference between groove contacts and the spatial pattern of groove contacts across the whiskers.

}, keywords = {stick/slip, texture classification task, touch, vibrissae, whisking}, doi = {10.1098/rstb.2011.0161}, author = {Yanfang Zuo and Igor Perkon and Mathew E. Diamond} }