Asymptotic derivation of a higher-order one-dimensional model for tape springs.

We derive a one-dimensional model for tape springs. The derivation starts from nonlinear thin-shell theory and uses a dimension reduction technique that combines a centreline-based parametrization of the tape-spring midsurface with the assumption that the strain varies slowly along the length of the tape spring. The one-dimensional model is effectively a higher-order rod model: at leading order, the strain energy depends on the extensional, bending and twisting strains and is consistent with classical results from the literature; the two following orders are novel and capture the dependence of the strain energy on the strain gradients.

Bending Response of a Book with Internal Friction.

We study the bending of a booklike system, comprising a stack of elastic plates coupled through friction. The behavior of this layered system is rich and nontrivial, with a nonadditive enhancement of the apparent stiffness and a significant hysteretic response. A dimension reduction procedure is employed to develop a centerline-based theory describing the stack as a nonlinear planar rod with internal shear.

A nonlinear beam model of photomotile structures.

Actuation remains a significant challenge in soft robotics. Actuation by light has important advantages: Objects can be actuated from a distance, distinct frequencies can be used to actuate and control distinct modes with minimal interference, and significant power can be transmitted over long distances through corrosion-free, lightweight fiber optic cables. Photochemical processes that directly convert photons to configurational changes are particularly attractive for actuation.

Shape-morphing architected sheets with non-periodic cut patterns.

We investigate the out-of-plane shape morphing capability of single-material elastic sheets with architected cut patterns that result in arrays of tiles connected by flexible hinges. We demonstrate that a non-periodic cut pattern can cause a sheet to buckle into three-dimensional shapes, such as domes or patterns of wrinkles, when pulled at specific boundary points. These global buckling modes are observed in experiments and rationalized by an in-plane kinematic analysis that highlights the role of the geometric frustration arising from non-periodicity.

The surprising dynamics of a chain on a pulley: lift off and snapping.

The motion of weights attached to a chain or string moving on a frictionless pulley is a classic problem of introductory physics used to understand the relationship between force and acceleration. Here, we consider the dynamics of the chain when one of the weights is removed and, thus, one end is pulled with constant acceleration. This simple change has dramatic consequences for the ensuing motion: at a finite time, the chain 'lifts off' from the pulley, and the free end subsequently accelerates than the end that is pulled.

Shape Transformations of Epithelial Shells.

Regulated deformations of epithelial sheets are frequently foreshadowed by patterning of their mechanical properties. The connection between patterns of cell properties and the emerging tissue deformations is studied in multiple experimental systems, but the general principles remain poorly understood. For instance, it is in general unclear what determines the direction in which the patterned sheet is going to bend and whether the resulting shape transformation will be discontinuous or smooth.

From discrete to continuum models of three-dimensional deformations in epithelial sheets.

Epithelial tissue, in which cells adhere tightly to each other and to the underlying substrate, is one of the four major tissue types in adult organisms. In embryos, epithelial sheets serve as versatile substrates during the formation of developing organs. Some aspects of epithelial morphogenesis can be adequately described using vertex models, in which the two-dimensional arrangement of epithelial cells is approximated by a polygonal lattice with an energy that has contributions reflecting the properties of individual cells and their interactions.

Liquid ropes: a geometrical model for thin viscous jet instabilities.

Thin, viscous fluid threads falling onto a moving belt behave in a way reminiscent of a sewing machine, generating a rich variety of periodic stitchlike patterns including meanders, W patterns, alternating loops, and translated coiling. These patterns form to accommodate the difference between the belt speed and the terminal velocity at which the falling thread strikes the belt. Using direct numerical simulations, we show that inertia is not required to produce the aforementioned patterns.

An introduction to the mechanics of the lasso.

Trick roping evolved from humble origins as a cattle-catching tool into a sport that delights audiences all over the world with its complex patterns or 'tricks'. Its fundamental tool is the lasso, formed by passing one end of a rope through a small loop (the honda) at the other end. Here, we study the mechanics of the simplest rope trick, the , in which the rope is driven by the steady circular motion of the roper's hand in a horizontal plane.

Furrow constriction in animal cell cytokinesis.

Cytokinesis is the process of physical cleavage at the end of cell division; it proceeds by ingression of an acto-myosin furrow at the equator of the cell. Its failure leads to multinucleated cells and is a possible cause of tumorigenesis. Here, we calculate the full dynamics of furrow ingression and predict cytokinesis completion above a well-defined threshold of equatorial contractility.

Solid drops: large capillary deformations of immersed elastic rods.

Under the effect of surface tension, a blob of liquid adopts a spherical shape when immersed in another fluid. We demonstrate experimentally that soft, centimeter-size elastic solids can exhibit a similar behavior: when immersed into a liquid, a gel having a low elastic modulus undergoes large, reversible deformations. We analyze three fundamental types of deformations of a slender elastic solid driven by surface stress, depending on the shape of its cross section: a circular elastic cylinder shortens in the longitudinal direction and stretches transversally; the sharp edges of a square based prism get rounded off as its cross sections tend to become circular; and a slender, triangular based prism bends.

Shape of an elastic loop strongly bent by surface tension: experiments and comparison with theory.

When a very flexible wire is dipped into a soapy solution, it collapses onto itself. We consider the regions of high curvature where the wire folds back onto itself, enclosing a capillary film. The shapes of these end loops are measured in experiments using soap films and compared to a known similarity solution.

Influence of Stratum Corneum on the entire skin mechanical properties, as predicted by a computational skin model.

Background/purpose: Skin mechanical properties are globally well described. The aim of this paper is to evaluate, by means of a numerical model, the influence of Stratum Corneum (SC) on skin folding resulting from an in-plane compression.

Methods: A computational skin model was developed where skin is divided into three layers (SC, epidermis and upper dermis, and deep dermis) of different thicknesses and elastic moduli.

Instant fabrication and selection of folded structures using drop impact.

A drop impacting a target cutout in a thin polymer film is wrapped by the film in a dynamic sequence involving both capillary forces and inertia. Different 3D structures can be produced from a given target by slightly varying the impact parameters. A simplified model for a nonlinear dynamic Elastica coupled with a drop successfully explains this shape selection and yields detailed quantitative agreement with experiments.

Fragmentation of rods by cascading cracks: why spaghetti does not break in half.

When thin brittle rods such as dry spaghetti pasta are bent beyond their limit curvature, they often break into more than two pieces, typically three or four. With the aim of understanding these multiple breakings, we study the dynamics of a bent rod that is suddenly released at one end. We find that the sudden relaxation of the curvature at this end leads to a burst of flexural waves, whose dynamics are described by a self-similar solution with no adjustable parameters.