arXiv subjects

John S. Biggins

Publications and source records attributed to John S. Biggins.

At least 19 recordsLinked to original sources

arXiv2026

Snapping and Switching of Elastic Arches with Patterned Preferred Curvature

An elastic arch is an archetypal bistable system. Here, we combine elastica theory and photo-mechanical experiments to elucidate the mechanics of an active arch with a spatio-temporally varying preferred curvature $\overline κ(s)$. Our shallow-arch theory completely describes any such system via the decomposition of its $\overline κ(s)$ into Euler-buckling modes. Intuitively, if $\overline κ(s)$ overlaps with the fundamental mode, it snaps the arch up/down. Conversely, non-overlapping $\overline κ(s)$ drives a second-order transition to a higher-order shape. Furthermore, the form of $\overline κ(s)$ enables control over the instability's character; we find the forms for snapping with maximum energy release and at the lowest stimulation (both binary patterns) and design forms for symmetric and asymmetric switching pathways. Analogous control can also be achieved in boundary-driven instabilities of passive arches by fabricating them with suitable $\overline κ(s)$. We thus anticipate our results will improve switchable/snapping elements in MEMS, robotics, and mechanical meta-materials.

cond-mat.soft↗

arXiv2025

Beyond mechanochromism: Programmable multimodal actuation in cholesteric liquid crystal elastomer hollow fibers

Cholesteric liquid crystal elastomers (CLCEs) change color under strain, offering attractive prospects for smart textiles, soft robotics, and photonic devices. However, the helical structure of CLCEs averages out the exceptional anisotropy and soft elasticity of their nematic parents, leaving little scope for also using the director orientation to program their thermal or mechanical actuation. Here, we develop programmable CLCE hollow fibers via an anisotropic deswelling-assisted template method. By integrating dynamic boronic ester bond exchange with mechanical force/pneumatic pressure-induced liquid crystal mesogen orientation, we are able to make CLCE fibers with overall longitudinal, circumferential, and twisted directors, while preserving enough residual periodicity to maintain their structural color. Inflation of these fibers then yields a range of motions (expansion, contraction, elongation, and twisting) accompanied by synchronous adaptive color changes. To explain these motions, we derive a membrane balloon model based on the non-ideal neo-classical LCE energy with suitable CLCE director profiles. The model successfully captures all the key mechanical features, including non-monotonicity and sub-criticality as a function of inflationary pressure. We thus confirm that the fiber's rich mechanochromic behavior originates from the combination of cholesteric color and nematic-like programmed soft elasticity. Our study thus transcends the limitations of traditional CLCE fibers by combining orientation encoding, soft elasticity, and pneumatic actuation to provide a new paradigm for the development of systems that change both shape and color in a bespoke and versatile way.

cond-mat.soft↗

arXiv2023

Surface instability in a nematic elastomer

Liquid crystal elastomers (LCEs) are soft phase-changing solids that exhibit large reversible contractions upon heating, Goldstone-like soft modes and resultant microstructural instabilities. We heat a planar LCE slab to isotropic, clamp the lower surface then cool back to nematic. Clamping prevents macroscopic elongation, producing compression and microstructure. We see that the free surface destabilizes, adopting topography with amplitude and wavelength similar to thickness. To understand the instability, we numerically compute the microstructural relaxation of a "non-ideal" LCE energy. Linear stability reveals a Biot-like scale-free instability, but with oblique wavevector. However, simulation and experiment show that, unlike classic elastic creasing, instability culminates in a cross-hatch without cusps or hysteresis, and is constructed entirely from low-stress soft modes.

cond-mat.soft↗

arXiv2023

Lifting, Loading, and Buckling in Conical Shells

Liquid crystal elastomer films that morph into cones are strikingly capable lifters. Thus motivated, we combine theory, numerics, and experiments to reexamine the load-bearing capacity of conical shells. We show that a cone squashed between frictionless surfaces buckles at a smaller load, even in scaling, than the classical Seide/Koiter result. Such buckling begins in a region of greatly amplified azimuthal compression generated in an outer boundary layer with oscillatory bend. Experimentally and numerically, buckling then grows sub-critically over the full cone. We derive a new thin-limit formula for the critical load, $\propto t^{5/2}$, and validate it numerically. We also investigate deep post-buckling, finding further instabilities producing intricate states with multiple Pogorelov-type curved ridges arranged in concentric-circles or Archimedean spirals. Finally, we investigate the forces exerted by such states, which limit lifting performance in active cones.

cond-mat.soft↗

arXiv2023

Geometry, mechanics and actuation of intrinsically curved folds

We combine theory and experiments to explore the kinematics and actuation of intrinsically curved folds (ICFs) in otherwise developable shells. Unlike origami folds, ICFs are not bending isometries of flat sheets, but arise via non-isometric processes (growth/moulding) or by joining sheets along curved boundaries. Experimentally, we implement both, first making joined ICFs from paper, then fabricating flat liquid crystal elastomer (LCE) sheets that morph into ICFs upon heating/swelling via programmed metric changes. Theoretically, an ICF's intrinsic geometry is defined by the geodesic curvatures on either side, $κ_{g_i}$. Given these, and a target 3D fold-line, one can construct the entire surface isometrically, and compute the bending energy. This construction shows ICFs are bending mechanisms, with a continuous family of isometries trading fold angle against fold-line curvature. In ICFs with symmetric $κ_{g_i}$, straightening the fold-line culminates in a fully-folded flat state that is deployable but weak, while asymmetric ICFs ultimately lock with a mechanically strong finite-angle. When unloaded, freely-hinged ICFs simply adopt the (thickness $t$ independent) isometry that minimizes the bend energy. In contrast, in LCE ICFs a competition between flank and ridge selects a ridge curvature that, unusually, scales as $t^{-1/7}$. Finally, we demonstrate how multiple ICFs can be combined in one LCE sheet, to create a versatile stretch-strong gripper that lifts $\sim$40x its own weight.

cond-mat.soft↗

arXiv2022

Interfacial metric mechanics: stitching patterns of shape change in active sheets

A flat sheet programmed with a planar pattern of spontaneous shape change will morph into a curved surface. Such metric mechanics is seen in growing biological sheets, and may be engineered in actuating soft matter sheets such as phase-changing liquid crystal elastomers (LCEs), swelling gels and inflating baromorphs. Here, we show how to combine multiple patterns in a sheet by stitching regions of different shape changes together piecewise along interfaces. This approach allows simple patterns to be used as building blocks, and enables the design of multi-material or active/passive sheets. We give a general condition for an interface to be geometrically compatible, and explore its consequences for LCE/LCE, gel/gel, and active/passive interfaces. In contraction/elongation systems such as LCEs, we find an infinite set of compatible interfaces between any pair of patterns along which the metric is discontinuous, and a finite number across which the metric is continuous. As an example, we find all possible interfaces between pairs of LCE logarithmic spiral patterns. In contrast, in isotropic systems such as swelling gels, only a finite number of continuous interfaces are available, greatly limiting the potential of stitching. In both continuous and discontinuous cases, we find the stitched interfaces generically carry singular Gaussian curvature, leading to intrinsically curved folds in the actuated surface. We give a general expression for the distribution of this curvature, and a more specialized form for interfaces in LCE patterns. The interfaces thus also have rich geometric and mechanical properties in their own right.

cond-mat.soft↗

arXiv2022

Curvature-driven instabilities in thin active shells

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 Gaussian curvature. We identify two types of super-critical symmetry breaking instability, in which the shell's principal curvature spontaneously breaks discrete up-down symmetry and continuous planar isotropy respectively. These are then augmented by inversion instabilities, in which the shell jumps sub-critically between up/down broken symmetry states, and rotation instabilities, in which the curvatures rotate by 90 degrees 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.

cond-mat.soft↗

arXiv2021

Evolving, complex topography from combining centers of Gaussian curvature

Liquid crystal elastomers and glasses can have significant shape change determined by their director patterns. Cones deformed from circular director patterns have non-trivial Gaussian curvature localised at tips, curved interfaces, and intersections of interfaces. We employ a generalised metric compatibility condition to characterize two families of interfaces between circular director patterns -- hyperbolic and elliptical interfaces, and find that the deformed interfaces are geometrically compatible. We focus on hyperbolic interfaces to design complex topographies and non-isometric origami, including n-fold intersections, symmetric and irregular tilings. The large design space of three-fold and four-fold tiling is utilized to quantitatively inverse design an array of pixels to display target images. Taken together, our findings provide comprehensive design principles for the design of actuators, displays, and soft robotics in liquid crystal elastomers and glasses.

cond-mat.soft↗

arXiv2021

Large deformation analysis of spontaneous twist and contraction in nematic elastomer fibres with helical director

A cylindrical rubber fibre subject to twist will also elongate: a manifestation of Poynting's effect in large strain elasticity. Here, we construct an analogous treatment for an active rubber fibre actuated via an axisymmetric pattern of spontaneous distortion. We start by constructing an exact large-deformation solution to the equations of elasticity for such fibre subject to imposed twist and stretch, which reveals spontaneous warping and twisting of the fibre 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 fibres 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. Secondly, we consider realistic director distributions for the experimentally reported fibres fabricated by cross-linking while simultaneously applying stretch and twist. Counter-intuitively, we find that maximum actuation twist is produced by applying a finite optimal twist during fabrication. Finally, we illustrate that spontaneously twisting fibres will coil into spring-like shapes on actuation if the ends are prevented from twisting relative to each other. Such twist-torsion coupling would allow to make a tendril-like "soft-spring" actuator with low force and high linear stroke compared to the intrinsic contraction of the elastomer itself.

cond-mat.soft↗

arXiv2020

Defective nematogenesis: Gauss curvature in programmable shape-responsive sheets with topological defects

Flat sheets encoded with patterns of contraction/elongation morph into curved surfaces. If the surfaces bear Gauss curvature, the resulting actuation can be strong and powerful. We deploy the Gauss-Bonnet theorem to deduce the Gauss curvature encoded in a pattern of uniform-magnitude contraction/elongation with spatially varying direction, as is commonly implemented in patterned liquid crystal elastomers. This approach reveals two fundamentally distinct contributions: a structural curvature which depends on the precise form of the pattern, and a topological curvature generated by defects in the contractile direction. These curvatures grow as different functions the contraction/elongation magnitude, explaining the apparent contradiction between previous calculations for simple +1 defects, and smooth defect-free patterns. We verify these structural and topological contributions by conducting numerical shell calculations on sheets encoded with simple higher-order contractile defects to reveal their activated morphology. Finally we calculate the Gauss curvature generated by patterns with spatially varying magnitude and direction, which leads to additional magnitude gradient contributions to the structural term. We anticipate this form will be useful whenever magnitude and direction are natural variables, including in describing the contraction of a muscle along its patterned fiber direction, or a tissue growing by elongating its cells.

cond-mat.soft↗

arXiv2020

Giant deformations and soft-inflation in LCE balloons

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.

cond-mat.soft↗

arXiv2020

Ballooning, bulging and necking: an exact solution for longitudinal phase separation in elastic systems near a critical point

Prominent examples of longitudinal phase separation in elastic systems include elastic necking, the propagation of a bulge in a cylindrical party balloon and the beading of a gel fiber subject to surface tension. Here we demonstrate that, if the parameters of such a system are tuned near a critical point (where the difference between the two phases vanishes) then the behaviour of all systems is given by the minimization of a simple and universal elastic energy familiar from Ginzburg-Landau theory in an external field. We minimize this energy analytically, which yields not only the well known interfacial tanh solution, but also the complete set of stable and unstable solutions in both finite and infinite length systems, unveiling the elastic system's full shape evolution and hysteresis. Correspondingly, we also find analytic results for the the delay of onset, changes in criticality and ultimate suppression of instability with diminishing system length, demonstrating that our simple near-critical theory captures much of the complexity and choreography of far-from-critical systems. Finally, we find critical points for the three prominent examples of phase separation given above, and demonstrate how each system then follows the universal set of solutions.

cond-mat.soft↗

arXiv2018

Peristaltic elastic instability in an inflated cylindrical channel

A long cylindrical cavity through a soft solid forms a soft microfluidic channel, or models a vascular capillary. We observe experimentally that, when such a channel bears a pressurized fluid, it first dilates homogeneously, but then becomes unstable to a peristaltic elastic instability. We combine theory and numerics to fully characterize the instability in a channel through a bulk neo-Hookean solid, showing that instability occurs supercritically with wavelength $2π/k=12.278....a$ when the pressure exceeds $2.052....μ$. In finite solids, the threshold pressure is reduced, and peristalsis is followed by a second instability which shears the peristaltic shape breaking axisymmetry. These instabilities shows that, counterintuitively, if a pipe runs through a bulk solid, the bulk solid can be destabilizing rather than stabilizing at high pressures. They also offers a route to fabricate periodically undulating channels, producing waveguides with photonic/phononic stop bands.

cond-mat.soft↗

arXiv2017

The Plateau-Rayleigh instability in solids is a simple phase separation

A long elastic cylinder, radius $a$ and shear-modulus $μ$, becomes unstable given sufficient surface tension $γ$. We show this instability can be simply understood by considering the energy, $E(λ)$, of such a cylinder subject to a homogenous longitudinal stretch $λ$. Although $E(λ)$ has a unique minimum, if surface tension is sufficient ($Γ\equivγ/(aμ)>\sqrt{32}$) it looses convexity in a finite region. We use a Maxwell construction to show that, if stretched into this region, the cylinder will phase separate into two segments with different stretches $λ_1$ and $λ_2$. Our model thus explains why the instability has infinite wavelength, and allows us to calculate the instability's sub-critical hysteresis loop (as a function of imposed stretch), showing that instability proceeds with constant amplitude and at constant (positive) tension as the cylinder is stretched between $λ_1$ and $λ_2$. We use full nonlinear finite-element calculations to verify these predictions, and to characterize the interface between the two phases. Near $Γ=\sqrt{32}$ the length of such an interface diverges introducing a new length-scale and allowing us to construct a 1-D effective theory. This treatment yields an analytic expression for the interface itself, revealing its characteristic length grows as $l_{wall}\sim a/\sqrt{Γ-\sqrt{32}}$.

cond-mat.soft↗

arXiv2015

Mechanics of invagination and folding: hybridized instabilities when one soft tissue grows on another

We address the folding induced by differential growth in soft layered solids via an elementary model that consists of a soft growing neo-Hookean elastic layer adhered to a deep elastic substrate. As the layer/substrate modulus ratio is varied from above unity towards zero we find a first transition from supercritical smooth folding followed by cusping of the valleys to direct subcritical cusped folding, then another to supercritical cusped folding. Beyond threshold the high amplitude fold spacing converges to about four layer thicknesses for many modulus ratios. In three dimensions the instability gives rise to a wide variety of morphologies, including almost degenerate zigzag and triple-junction patterns that can coexist when the layer and substrate are of comparable softness. Our study unifies these results providing understanding for the complex and diverse fold morphologies found in biology, including the zigzag precursors to intestinal villi, and disordered zigzags and triple-junctions in mammalian cortex.

cond-mat.soft↗

arXiv2015

Gyrification from constrained cortical expansion

The exterior of the mammalian brain - the cerebral cortex - has a conserved layered structure whose thickness varies little across species. However, selection pressures over evolutionary time scales have led to cortices that have a large surface area to volume ratio in some organisms, with the result that the brain is strongly convoluted into sulci and gyri. Here we show that the gyrification can arise as a nonlinear consequence of a simple mechanical instability driven by tangential expansion of the gray matter constrained by the white matter. A physical mimic of the process using a layered swelling gel captures the essence of the mechanism, and numerical simulations of the brain treated as a soft solid lead to the formation of cusped sulci and smooth gyri similar to those in the brain. The resulting gyrification patterns are a function of relative cortical expansion and relative thickness (compared with brain size), and are consistent with observations of a wide range of brains, ranging from smooth to highly convoluted. Furthermore, this dependence on two simple geometric parameters that characterize the brain also allows us to qualitatively explain how variations in these parameters lead to anatomical anomalies in such situations as polymicrogyria, pachygyria, and lissencephalia.

physics.bio-ph↗

arXiv2014

Surface sulci in squeezed soft solids

The squeezing of soft solids, the constrained growth of biological tissues, and the swelling of soft elastic solids such as gels can generate large compressive stresses at their surfaces. This causes the otherwise smooth surface of such a solid to becomes unstable when its stress exceeds a critical value. Previous analyses of the surface instability have assumed two-dimensional plane-strain conditions, but in experiments isotropic stresses often lead to complex three-dimensional sulcification patterns. Here we show how such diverse morphologies arise by numerically modeling the lateral compression of a rigidly clamped elastic layer. For incompressible solids, close to the instability threshold, sulci appear as I-shaped lines aligned orthogonally with their neighbors; at higher compressions they are Y-shaped and prefer a hexagonal arrangement. In contrast, highly compressible solids when squeezed show only one sulcified phase characterized by a hexagonal sulcus network.

cond-mat.soft↗

arXiv2014

Growth and Shape of a Chain Fountain

If a long chain is held in a pot elevated a distance h_1 above the floor, and the end of the chain is then dragged over the rim of the pot and released, the chain flows under gravity down into a pile on the floor. Not only does the chain flow out of the pot, it also leaps above the pot in a "chain-fountain". I predict and observe that if the pot is held at an angle to the vertical the steady state shape of the fountain is an inverted catenary, and discuss how to apply boundary conditions to this solution. In the case of a level pot, the fountain shape is completely vertical. In this case I predict and observe both how fast the fountain grows to its steady state hight, and how it grows quadratically in time if there is no floor. The fountain is driven by an anomalous push force from the pot that acts on the link of chain about to come into motion. I confirm this by designing two new chains, one consisting of hollow cylinders threaded on a string and one consisting of heavy beads separated by long flexible threads. The former is predicted to produce a pot-push and hence a fountain, while the latter will not. I confirm these predictions experimentally. Finally I directly observe the anomalous push in a horizontal chain-pick up experiment.

physics.class-ph↗