Tuomas Tallinen

Villification: How the Gut Gets Its Villi

Intestinal Villus Formation The intestinal villi are essential elaborations of the lining of the gut that increase the epithelial surface area for nutrient absorption. Shyer et al. (p. 212, published online 29 August; see the Perspective by Simons) show that in both the developing human and chick gut, the villi are formed in a step-wise progression, involving the sequential folding of the endoderm into longitudinal ridges, via a zigzag pattern, to finally form individual villi. These changes are established through the differentiation of the smooth muscle layers of the gut, restricting the expansion of the adjacent proliferating and growing endoderm and mesenchyme, generating compressive stresses that lead to the buckling and folding of the tissue. Muscular control over proliferating mesenchyme and epithelium yields intestinal villi. [Also see Perspective by Simons] The villi of the human and chick gut are formed in similar stepwise progressions, wherein the mesenchyme and attached epithelium first fold into longitudinal ridges, then a zigzag pattern, and lastly individual villi. We find that these steps of villification depend on the sequential differentiation of the distinct smooth muscle layers of the gut, which restrict the expansion of the growing endoderm and mesenchyme, generating compressive stresses that lead to their buckling and folding. A quantitative computational model, incorporating measured properties of the developing gut, recapitulates the morphological patterns seen during villification in a variety of species. These results provide a mechanistic understanding of the formation of these elaborations of the lining of the gut, essential for providing sufficient surface area for nutrient absorption.

Twisting graphene nanoribbons into carbon nanotubes

Although carbon nanotubes consist of honeycomb carbon, they have never been fabricated from graphene directly. Here, it is shown by quantum molecular-dynamics simulations and classical continuum-elasticity modeling, that graphene nanoribbons can, indeed, be transformed into carbon nanotubes by means of twisting. The chiralities of the tubes thus fabricated can be not only predicted but also externally controlled. This twisting route is an opportunity for nanofabrication, and is easily generalizable to ribbons made of other planar nanomaterials.

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 become 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.

The effect of plasticity in crumpling of thin sheets

Crumpling a thin sheet of material into a small volume requires energy for creating a network of deformations such as vertices and ridges. Scaling properties of a single elastic vertex or ridge have been analysed theoretically, and crumpling of a sheet by numerical simulations. Real materials are however elasto-plastic and large local strains induce irreversible plastic deformations. Hence, a numerical model that can be purely elastic or elasto-plastic is introduced. In crumpled elastic sheets, the ridge patterns are found to be similar, independent of the width to thickness (L/h) ratio of the sheet, and the fractal dimension of crumpled sheets is given by scaling properties of the energy and average length of ridges. In crumpled elasto-plastic sheets, such a similarity does not appear as the L/h ratio affects the deformations, and the fractal dimension (Dpl) is thereby reduced. Evidence is also found of Dpl not being universal but dependent on the plastic yield point of the material.

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-to-substrate modulus ratio is varied from above unity toward 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.

A discrete-element model for viscoelastic deformation and fracture of glacial ice

a b s t r a c t A discrete-element model was developed to study the behavior of viscoelastic materials that are allowed to fracture. Applicable to many materials, the main objective of this analysis was to develop a model specifically for ice dynamics. A realistic model of glacial ice must include elasticity, brittle fracture and slow viscous deformations. Here the model is described in detail and tested with several benchmark simulations. The model was used to simulate various ice-specific applications with resulting flow rates that were compatible with Glens law, and produced under fragmentation fragment-size distributions that agreed with the known analytical and experimental results.

Shock-driven jamming and periodic fracture of particulate rafts

A tenuous monolayer of hydrophobic particles at the air-water interface often forms a scum or raft. When such a monolayer is disturbed by the localized introduction of a surfactant droplet, a radially divergent surfactant shock front emanates from the surfactant origin and packs the particles into a jammed, compact, annular band with a packing fraction that saturates at a peak packing fraction *. As the resulting two-dimensional, disordered elastic band grows with time and is driven radially outwards by the surfactant, it fractures to form periodic triangular cracks with robust geometrical features. We find that the number of cracks N and the compaction band radius R* at fracture onset vary monotonically with the initial packing fraction (init). However, the compaction bands width W* is constant for all init. A simple geometric theory that treats the compaction band as an elastic annulus, and accounts for mass conservation allows us to deduce that N2πR*/W*4πRCP/init, a result we verify both experimentally and numerically. We show that the essential ingredients for this phenomenon are an initially low enough particulate packing fraction that allows surfactant-driven advection to cause passive jamming and eventual fracture of the hydrophobic particulate interface.

Forced tearing of ductile and brittle thin sheets

Tearing a thin sheet by forcing a rigid object through it leads to complex crack morphologies; a single oscillatory crack arises when a tool is driven laterally through a brittle sheet, while two diverging cracks and a series of concertinalike folds forms when a tool is forced laterally through a ductile sheet. On the other hand, forcing an object perpendicularly through the sheet leads to radial petallike tears in both ductile and brittle materials. To understand these different regimes we use a combination of experiments, simulations, and simple theories. In particular, we describe the transition from brittle oscillatory tearing via a single crack to ductile concertina tearing with two tears by deriving laws that describe the crack paths and wavelength of the concertina folds and provide a simple phase diagram for the morphologies in terms of the material properties of the sheet and the relative size of the tool.

Discrete element simulations of crumpling of thin sheets

Forced crumpling of stiff self-avoiding sheets is studied by discrete element simulations. Simulations display stress condensation and scaling of ridge energy in agreement with theoretical expectations for elastic and frictionless sheets, and extends such behavior to elasto-plastic sheets. Crumpling of ideally elastic and frictionless sheets is compared to that of elasto-plastic sheets and sheets with friction.