Mechanical and Thermal Stability of Adhesive Membranes with Nonzero Bending Rigidity

Membranes at a microscopic scale are affected by thermal fluctuations and self-adhesion due to van der Waals forces. Methods to prepare membranes of even molecular scale, e.g., graphene, have recently been developed, and the question of their mechanical and thermal stability is of crucial importance. To this end we modeled microscopic membranes with an attractive interaction and applied Langevin dynamics. Their behavior was also analyzed under external loading. Even though these membranes folded during isotropic compression as a result of energy minimization, the process at high confinement was similar to crumpling of macroscopic nonadhesive sheets. The main difference appeared when the com…

Scaling Behavior in Non-Hookean Compression of Thin-Walled Structures

The mechanics and stability of thin-walled structures is a challenging and important branch in structural mechanics. Under vertical compression the deformation of a thin-walled box differs from that of, e.g., a cylindrical shell. It is demonstrated here that compression of a box can be described by a set of generic scaling laws representing three successive regimes: a linear, wrinkled, and collapsed regime. The linear Hookean regime represents the normal behavior before any instability sets in, while the following wrinkled regime is shown to be analogous to compression of thin-film blisters. The compression force reaches its maximum at the onset of the final collapsed regime that has all th…

Deterministic folding in stiff elastic membranes.

Crumpled membranes have been found to be characterized by complex patterns of spatially seemingly random facets separated by narrow ridges of high elastic energy. We demonstrate by numerical simulations that compression of stiff elastic membranes with small randomness in their initial configurations leads to either random ridge configurations (high entropy) or nearly deterministic folds (low elastic energy). For folding with symmetric ridge configurations to appear in part of the crumpling processes, the crumpling rate must be slow enough. Folding stops when the thickness of the folded structure becomes important, and crumpling continues thereafter as a random process.

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 Glen's law, and produced under fragmentation fragment-size distributions that agreed with the known analytical and experimental results.

Numerical model for the shear rheology of two-dimensional wet foams with deformable bubbles

Shearing of two-dimensional wet foam is simulated using an introduced numerical model, and results are compared to those of experiments. This model features realistically deformable bubbles, which distinguishes it from previously used models for wet foam. The internal bubble dynamics and their contact interactions are also separated in the model, making it possible to investigate the effects of the related microscale properties of the model on the macroscale phenomena. Validity of model assumptions was proved here by agreement between the simulated and measured Herschel-Bulkley rheology, and shear-induced relaxation times. This model also suggests a relationship between the shear stress and…

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 a…

The effect of plasticity in crumpling of thin sheets

Bridging the gap between theoretical and experimental work to understand the effect of plasticity on the crumpling of thin sheets into a small volume has proved difficult. A realistic numerical model now makes a distinction between elastic and elasto-plastic behaviour. Crumpling a thin sheet of material into a small volume requires energy for creating a network of deformations such as vertices and ridges1,2. Scaling properties of a single elastic vertex3,4,5 or ridge have been analysed theoretically6,7,8, and crumpling of a sheet by numerical simulations1,9,10. Real materials are however elasto-plastic11,12,13,14,15 and large local strains induce irreversible plastic deformations. Hence, a …

Contact formation in random networks of elongated objects

The effect of steric hindrance is an important aspect of granular packings as it gives rise to, e.g., limitations on the densities of ordered and disordered packings, both of which are essentially defined by the geometry of the constituents. Here we focus on random packing of rods via deposition and their distributions of contact number and segment length. Such statistical properties are relevant for mechanical properties of the structures, but the (quite large) steric effects on them have not been addressed in previous studies. We therefore develop a theory that describes the statistical properties of rod packings, while taking into account that the deposited rods cannot overlap and thus i…

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 …

On the growth and form of cortical convolutions

International audience; The rapid growth of the human cortex during development is accompanied by the folding of the brain into a highly convoluted structure1-3. Recent studies have focused on the genetic and cellular regulation of cortical growth4-8, but understanding the formation of the gyral and sulcal convolutions also requires consideration of the geometry and physical shaping of the growing brain9-15. To study this, we use magnetic resonance images to build a 3D-printed layered gel mimic of the developing smooth fetal brain; when immersed in a solvent, the outer layer swells relative to the core, mimicking cortical growth. This relative growth puts the outer layer into mechanical com…

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.

Elastic configurations of self-supported oxide membranes for fuel cells

Abstract Ultra-thin oxide films are of interest in energy conversion technologies such as low temperature solid oxide fuel cells and permeation membranes. Understanding their thermo-mechanical stability is an important problem. Edge clamped, self-supported thin film membranes show hierarchical wrinkles; with the largest wavelengths in the center, while smaller ones arise near the clamped boundary; correspondingly the largest strains, with tensile stress comparable to the residual stress, are in the vicinity of the clamped boundary. Our results can be understood by simple scaling arguments and are valid for membranes in the post-buckling regime far from threshold. We confirm the validity of …

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 thresho…

Contact formation in random networks of elongated objects

The effect of steric hindrance is an important aspect of granular packings as it gives rise to, e.g., limitations on the densities of ordered and disordered packings, both of which are essentially defined by the geometry of the constituents. Here we focus on the random packing of rods via deposition and their distributions of contact number and segment length. Such statistical properties are relevant for mechanical properties of the structures, but the (quite large) steric effects on them have not been addressed in previous studies. We therefore develop a theory that describes the statistical properties of rod packings, while taking into account that the deposited rods cannot overlap and th…

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.

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-ju…

A particle based simulation model for glacier dynamics

This publication is contribution number 22 of the Nordic Centre of Excellence SVALI, “Stability and Variations of Arctic Land Ice”, funded by the Nordic Top-level Research Initiative (TRI). The work has been supported by the SVALI project through the University of Lapland, Arctic Centre, and through the University Centre in Svalbard. Funding was also provided by the Conoco-Phillips and Lunding High North Research Program (CRIOS: Calving Rates and Impact on Society). A particle-based computer simulation model was developed for investigating the dynamics of glaciers. In the model, large ice bodies are made of discrete elastic particles which are bound together by massless elastic beams. These…

Numerical studies on membrane crumpling