A cylindrical rubber fiber subject to a twist will also elongate: a manifestation of Poynting’s effect in large strain elasticity. Here, we construct an analogous treatment for an active rubber fiber actuated via an axisymmetric pattern of spontaneous distortion. We start by constructing an exact large-deformation solution to the equations of elasticity for such fiber subject to imposed twist and stretch, which reveals spontaneous warping and twisting of the fiber cross section absent in passive rubbers. We then compute the corresponding non-linear elastic energy, which encompasses the Poynting effect but is minimized by a finite spontaneous twist and stretch. In the second half of the paper, we apply these results to understand the twist-contraction actuation of nematic elastomer fibers fabricated with director fields that encode helical patterns of contraction on heating. We first consider patterns making a constant angle with respect to the local cylindrical coordinate system (conical spiral director curves) and verify the predicted spontaneous twist, contraction, and cross-section deformation via finite elements. Second, we consider realistic director distributions for the experimentally reported fibers fabricated by cross-linking while simultaneously applying stretch and twist. Counterintuitively, we find that the maximum actuation twist is produced by applying a finite optimal twist during fabrication. Finally, we illustrate that spontaneously twisting fibers will coil into spring-like shapes on actuation if the ends are prevented from twisting relative to each other. Such a twist–torsion coupling would allow us to make a tendril-like “soft-spring” actuator with low force and high linear stroke compared to the intrinsic contraction of the elastomer itself.
We propose that ballooning can be controlled, enriched and amplified by using rubbery networks of aligned molecular rods known as liquid crystal elastomers (LCEs). Firstly, LCEs are promising artificial muscles, showing large spontaneous deformations in response to heat and light. In LCE balloons, spontaneous deformations can trigger classic ballooning, either as phase separation (at constant volume) or a volume jump (at constant pressure), resulting in greatly magnified actuation strains. Secondly, even at constant temperature, LCEs have unusual mechanics augmented by soft modes of deformation in which the nematic director rotates within the elastomer. These soft modes enrich the mechanics of LCE balloons, which can also “balloon” between rotated and unrotated states, either during the classic instability, or as a separate pre-cursor, leading to successive instabilities during inflation.
Liquid crystal elastomers (LCEs) undergo a large uniaxial contraction upon thermal or optical stimulation. LCE sheets are often fabricated with a spatially patterned direction of contraction, which can sculpt the sheet into a Gauss-curved surface. Here, we instead consider LCE sheets subject to patterned stimulation intensity, leading to a control of contraction strength. We show such patterns may similarly sculpt a complex surface, but with the advantage that arbitrarily many surfaces may be achieved sequentially in the same sample, thus breaking the link between microstructure and shape adaptivity. We first consider a monodomain LCE in which some regions are actuated and others are not. We discuss how to join actuated and unactuated regions compatibly, and use this design rule to generate patterns for cones, anti-cones, arrays of cones, and a wine-bottle. We validate the patterns numerically via elastic shell simulations and demonstrate them experimentally via patterned photo-chemical actuation. Secondly, we consider an LCE disk with an azimuthal director profile actuated by a radially varying stimulus. We show, theoretically and numerically, how to design a stimulation profile to sculpt any surface of revolution. Such reconfigurable actuation offers enticing possibilities for haptics, robotics and locomotion.
Spontaneous material shape changes, such as swelling, growth or thermal expansion, can be used to trigger dramatic elastic instabilities in thin shells. These instabilities originate in geometric incompatibility between the preferred extrinsic and intrinsic curvature of the shell, which may be modified by active deformations through the thickness and in plane, respectively. Here, we solve the simplest possible model of such instabilities, which assumes the shells are shallow, thin enough to bend but not stretch, and subject to homogeneous preferred curvatures. We consider separately the cases of zero, positive and negative Gauss curvature. We identify two types of supercritical symmetry-breaking instability, in which the shell’s principal curvature spontaneously breaks discrete up/down symmetry and continuous planar isotropy. These are then augmented by inversion instabilities, in which the shell jumps subcritically between up/down broken symmetry states and rotation instabilities, in which the curvatures rotate by 90° between states of broken isotropy without release of energy. Each instability has a thickness-independent threshold value for the preferred extrinsic curvature proportional to the square root of Gauss curvature. Finally, we show that the threshold for the isotropy-breaking instability is the same for deep spherical caps, in good agreement with recently published data.
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