@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 {68, title = {Optimal design of planar shapes with active materials}, journal = {Proceedings of the Royal Society A}, volume = {478}, year = {2022}, pages = {20220256}, abstract = {

Active materials have emerged as valuable candidates for shape morphing applications, where a body reconfiguration is achieved upon triggering its active response. Given a desired shape change, a natural question is to compare different morphing mechanisms to select the most effective one with respect to an optimality criterion. We introduce an optimal control problem to determine the active strains suitable to attain a target equilibrium shape while minimizing the complexity of the activation. Specifically, we discuss the planar morphing of active, hyperelastic bodies in the absence of external forces and exploit the notion of target metric to encompass a broad set of active materials in a unifying approach. For the case of affine shape changes, we derive explicit conditions on the body reference configuration for the optimality of homogeneous target metrics. More complex shape changes are analysed via numerical simulations to explore the impact on optimal solutions of different objective functionals inspired by features of existing materials. We show how stresses arising from incompatibilities contribute to reduce the complexity of the controls. We believe that our approach may be exploited for the optimal design of active systems and may contribute to gather insight into the morphing strategies of biological systems.\ 

}, keywords = {active materials, constrained optimization, shape morphing}, doi = {10.1098/rspa.2022.0256}, author = {Dario Andrini and Giovanni Noselli and Alessandro Lucantonio} } @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 {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 {60, title = {A theoretical study on the transient morphing of linear poroelastic plates}, journal = {Journal of Applied Mechanics}, volume = {In press}, year = {2020}, abstract = {

Based on their shape-shifting capabilities, soft active materials have enabled new possibilities for the engineering of sensing and actuation devices. While the relation between active strains and emergent equilibrium shapes has been fully characterized, the transient morphing of thin structures is a rather unexplored topic. Here, we focus on polymer gel plates and derive a reduced linear model to study their time-dependent response to changes in the fluid environment. We show that independent control of stretching and bending deformations in stress-free conditions allows to realize spherical shapes with prescribed geometry of the mid-plane. Further, we demonstrate that tensile (compressive) membrane stresses delay (accelerate) swelling-induced shape transitions, as compared to the stress-free evolution. We believe that these effects should be considered for the accurate design of smart systems and may contribute to explain the complexity of natural shapes.\ 

}, keywords = {Dimensional reduction, Polymer gel plates, Sensing and actuation devices, Shape-shifting structures, Transient morphing}, doi = {10.1115/1.4048806}, author = {Dario Andrini and Alessandro Lucantonio and Giovanni Noselli} } @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 {43, title = {Concurrent factors determine toughening in the hydraulic fracture of poroelastic composites}, journal = {Meccanica}, volume = {52}, year = {2017}, pages = {3489-3498}, abstract = {

Brittle materials fail catastrophically. In consequence of their limited flaw-tolerance, failure occurs by localized fracture and is typically a dynamic process. Recently, experiments on epithelial cell monolayers have revealed that this scenario can be significantly modified when the material susceptible to cracking is adhered to a hydrogel substrate. Thanks to the hydraulic coupling between the brittle layer and the poroelastic substrate, such a composite can develop a toughening mechanism that relies on the simultaneous growth of multiple cracks. Here, we study this remarkable behaviour by means of a detailed model, and explore how the material and loading parameters concur in determining the macro- scopic toughness of the system. By extending a previous study, our results show that rapid loading conveys material toughness by promoting distributed cracking. Moreover, our theoretical findings may suggest innovative architectures of flaw-insensitive materials with higher toughness.\ 

}, keywords = {brittle layer, cohesive zone, fracture, hydraulic fracture, hydrogel, multiple-cracking, toughening}, doi = {10.1007/s11012-017-0621-5}, author = {Alessandro Lucantonio and Giovanni Noselli} } @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 {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 {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 {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 {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} }