01815nas a2200145 4500008004100000245005800041210005800099300001300157490000800170520135300178100001901531700002201550700002701572856007001599 2022 eng d00aOptimal design of planar shapes with active materials0 aOptimal design of planar shapes with active materials a202202560 v4783 a

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.

1 aAndrini, Dario1 aNoselli, Giovanni1 aLucantonio, Alessandro uhttps://royalsocietypublishing.org/doi/abs/10.1098/rspa.2022.025601464nas a2200157 4500008004100000022001400041245007900055210006900134260000700203490000700210520098300217100001901200700002701219700002201246856003801268 2020 eng d a0021-893600aA Theoretical Study on the Transient Morphing of Linear Poroelastic Plates0 aTheoretical Study on the Transient Morphing of Linear Poroelasti c120 v883 a

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.

1 aAndrini, Dario1 aLucantonio, Alessandro1 aNoselli, Giovanni uhttps://doi.org/10.1115/1.404880602026nas a2200205 4500008004100000022001400041245009500055210006900150300001100219520136500230653002001595653002401615653001701639653002101656100002501677700002701702700002201729700002201751856004701773 2019 eng d a0022-509600aNutations in growing plant shoots: The role of elastic deformations due to gravity loading0 aNutations in growing plant shoots The role of elastic deformatio a1037023 a

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.

10aCircumnutations10aFlutter instability10aGravitropism10aHopf bifurcation1 aAgostinelli, Daniele1 aLucantonio, Alessandro1 aNoselli, Giovanni1 aDeSimone, Antonio uhttps://doi.org/10.1016/j.jmps.2019.10370200438nas a2200121 4500008004100000245005000041210005000091100002600141700002200167700002700189700001900216856008100235 2018 eng d00aFoldable structures made of hydrogel bilayers0 aFoldable structures made of hydrogel bilayers1 aAgostiniani, Virginia1 aDeSimone, Antonio1 aLucantonio, Alessandro1 aLučić, Danka uhttps://math.sissa.it/publication/foldable-structures-made-hydrogel-bilayers00566nas a2200121 4500008004100000245011800041210006900159260001700228100002600245700002700271700001900298856012700317 2018 eng d00aHeterogeneous elastic plates with in-plane modulation of the target curvature and applications to thin gel sheets0 aHeterogeneous elastic plates with inplane modulation of the targ bEDP Sciences1 aAgostiniani, Virginia1 aLucantonio, Alessandro1 aLučić, Danka uhttps://math.sissa.it/publication/heterogeneous-elastic-plates-plane-modulation-target-curvature-and-applications-thin-gel01712nas a2200229 4500008004100000022001400041245010200055210006900157300001200226490000800238520097600246653001601222653002001238653001601258653002201274100001601296700002701312700002701339700002201366700002201388856007201410 2018 eng d a0020-740300aSpontaneous morphing of equibiaxially pre-stretched elastic bilayers: The role of sample geometry0 aSpontaneous morphing of equibiaxially prestretched elastic bilay a481-4860 v1493 a

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.

10aBifurcation10aElastic bilayer10aPre-stretch10aShape programming1 aCaruso, Noe1 aCvetković, Aleksandar1 aLucantonio, Alessandro1 aNoselli, Giovanni1 aDeSimone, Antonio uhttps://www.sciencedirect.com/science/article/pii/S002074031731176101081nas a2200145 4500008004100000245007400041210006900115260003100184520057600215100002700791700002100818700002300839700002200862856005100884 2014 en d00aBuckling dynamics of a solvent-stimulated stretched elastomeric sheet0 aBuckling dynamics of a solventstimulated stretched elastomeric s bRoyal Society of Chemistry3 aWhen 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.1 aLucantonio, Alessandro1 aRoché, Matthieu1 aNardinocchi, Paola1 aStone, Howard, A. uhttp://urania.sissa.it/xmlui/handle/1963/3496701169nas a2200133 4500008004100000245007700041210006900118260003400187520069100221100002700912700002300939700002200962856005100984 2014 en d00aSwelling dynamics of a thin elastomeric sheet under uniaxial pre-stretch0 aSwelling dynamics of a thin elastomeric sheet under uniaxial pre bAmerican Institute of Physics3 aIt 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.1 aLucantonio, Alessandro1 aNardinocchi, Paola1 aStone, Howard, A. uhttp://urania.sissa.it/xmlui/handle/1963/3511301394nas a2200133 4500008004100000245006500041210006400106260002800170520094000198100002701138700002301165700002101188856005101209 2014 en d00aSwelling-induced and controlled curving in layered gel beams0 aSwellinginduced and controlled curving in layered gel beams bRoyal Society of London3 aWe 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.1 aLucantonio, Alessandro1 aNardinocchi, Paola1 aPezzulla, Matteo uhttp://urania.sissa.it/xmlui/handle/1963/34987