%0 Journal Article %J Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences %D 2022 %T Optimal design of planar shapes with active materials %A Dario Andrini %A Giovanni Noselli %A Alessandro Lucantonio %X

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.

%B Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences %V 478 %P 20220256 %G eng %U https://royalsocietypublishing.org/doi/abs/10.1098/rspa.2022.0256 %R 10.1098/rspa.2022.0256 %0 Journal Article %J Journal of Applied Mechanics %D 2020 %T A Theoretical Study on the Transient Morphing of Linear Poroelastic Plates %A Dario Andrini %A Alessandro Lucantonio %A Giovanni Noselli %X

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.

%B Journal of Applied Mechanics %V 88 %8 12 %G eng %U https://doi.org/10.1115/1.4048806 %R 10.1115/1.4048806 %0 Journal Article %J Journal of the Mechanics and Physics of Solids %D 2019 %T Nutations in growing plant shoots: The role of elastic deformations due to gravity loading %A Daniele Agostinelli %A Alessandro Lucantonio %A Giovanni Noselli %A Antonio DeSimone %K Circumnutations %K Flutter instability %K Gravitropism %K Hopf bifurcation %X

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’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.

%B Journal of the Mechanics and Physics of Solids %P 103702 %G eng %U https://doi.org/10.1016/j.jmps.2019.103702 %R 10.1016/j.jmps.2019.103702 %0 Report %D 2018 %T Foldable structures made of hydrogel bilayers %A Virginia Agostiniani %A Antonio DeSimone %A Alessandro Lucantonio %A Danka Lučić %G eng %0 Journal Article %J ESAIM: Control, Optimisation and Calculus of Variations %D 2018 %T Heterogeneous elastic plates with in-plane modulation of the target curvature and applications to thin gel sheets %A Virginia Agostiniani %A Alessandro Lucantonio %A Danka Lučić %B ESAIM: Control, Optimisation and Calculus of Variations %I EDP Sciences %G eng %R https://doi.org/10.1051/cocv/2018046 %0 Journal Article %J International Journal of Mechanical Sciences %D 2018 %T Spontaneous morphing of equibiaxially pre-stretched elastic bilayers: The role of sample geometry %A Noe Caruso %A Aleksandar Cvetković %A Alessandro Lucantonio %A Giovanni Noselli %A Antonio DeSimone %K Bifurcation %K Elastic bilayer %K Pre-stretch %K Shape programming %X

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.

%B International Journal of Mechanical Sciences %V 149 %P 481-486 %G eng %U https://www.sciencedirect.com/science/article/pii/S0020740317311761 %R https://doi.org/10.1016/j.ijmecsci.2017.08.049 %0 Journal Article %D 2014 %T Buckling dynamics of a solvent-stimulated stretched elastomeric sheet %A Alessandro Lucantonio %A Matthieu Roché %A Paola Nardinocchi %A Howard A. Stone %X When stretched uniaxially, a thin elastic sheet may exhibit buckling. The occurrence of buckling depends on the geometrical properties of the sheet and the magnitude of the applied strain. Here we show that an elastomeric sheet initially stable under uniaxial stretching can destabilize when exposed to a solvent that swells the elastomer. We demonstrate experimentally and computationally that the features of the buckling pattern depend on the magnitude of stretching, and this observation offers a new way for controlling the shape of a swollen homogeneous thin sheet. %I Royal Society of Chemistry %G en %U http://urania.sissa.it/xmlui/handle/1963/34967 %1 35197 %2 Physics %4 1 %$ Submitted by gfeltrin@sissa.it (gfeltrin@sissa.it) on 2015-11-10T09:50:41Z No. of bitstreams: 1 preprint2014.pdf: 2111018 bytes, checksum: 568652d2ca6c44cdad3e520342c8042d (MD5) %R 10.1039/c3sm52941j %0 Journal Article %D 2014 %T Swelling dynamics of a thin elastomeric sheet under uniaxial pre-stretch %A Alessandro Lucantonio %A Paola Nardinocchi %A Howard A. Stone %X It has been demonstrated experimentally that pre-stretch affects the swelling of an elastomeric membrane when it is exposed to a solvent. We study theoretically the one-dimensional swelling of a pre-stretched thin elastomeric sheet, bonded to an impermeable rigid substrate, to quantify the influence of pre-stretch. We show that the solvent uptake increases when pre-stretch increases, both at equilibrium and during the swelling transient, where it exhibits two different scaling regimes. The coupling between the solvent uptake and pre-stretch may be practically exploited to design soft actuators where the swelling-induced deformations can be controlled by varying the pre-stretch. %I American Institute of Physics %G en %U http://urania.sissa.it/xmlui/handle/1963/35113 %1 35370 %2 Physics %4 1 %$ Submitted by gfeltrin@sissa.it (gfeltrin@sissa.it) on 2015-12-02T16:28:53Z No. of bitstreams: 1 art2014.pdf: 777840 bytes, checksum: 2362b6250fd872264208d0d3b846a551 (MD5) %R 10.1063/1.4866576 %0 Journal Article %D 2014 %T Swelling-induced and controlled curving in layered gel beams %A Alessandro Lucantonio %A Paola Nardinocchi %A Matteo Pezzulla %X We describe swelling-driven curving in originally straight and non-homogeneous beams. We present and verify a structural model of swollen beams, based on a new point of view adopted to describe swelling-induced deformation processes in bilayered gel beams, that is based on the split of the swelling-induced deformation of the beam at equilibrium into two components, both depending on the elastic properties of the gel. The method allows us to: (i) determine beam stretching and curving, once assigned the characteristics of the solvent bath and of the non-homogeneous beam, and (ii) estimate the characteristics of non-homogeneous flat gel beams in such a way as to obtain, under free-swelling conditions, three-dimensional shapes. The study was pursued by means of analytical, semi-analytical and numerical tools; excellent agreement of the outcomes of the different techniques was found, thus confirming the strength of the method. %I Royal Society of London %G en %U http://urania.sissa.it/xmlui/handle/1963/34987 %1 35229 %2 Mathematics %4 1 %$ Approved for entry into archive by Lucio Lubiana (lubiana@sissa.it) on 2015-11-12T09:25:24Z (GMT) No. of bitstreams: 0 %R 10.1098/rspa.2014.0467