@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 {61, title = {A theoretical study on the transient morphing of linear poroelastic plates}, journal = {Journal of Applied Mechanics}, volume = {88}, year = {2021}, pages = {031008}, 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. Furthermore, we demonstrate that tensile (compressive) membrane stresses delay (accelerate) swelling-induced shape transitions 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 = {Andrini, Dario and Lucantonio, Alessandro and Noselli, Giovanni} } @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 {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 {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 {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} }