Related papers: Finite curved creases in infinite isometric sheets
Self-contractedness (or self-expandedness, depending on the orientation) is hereby extended in two natural ways giving rise, for any $\lambda\in\lbrack-1,1)$, to the metric notion of $\lambda $-curve and the (weaker) geometric notion of…
We examine the fracture mechanics of tearing graphene. We present a molecular dynamics simulation of the propagation of cracks in clamped, free-standing graphene as a function of the out-of-plane force. The geometry is motivated by…
Modeling of wrinkles and folds formation in single and multilayer graphene sheets lying on flat deformable (polymer) substrates has been carried out. It is shown that the deformability of the substrate leads to the appearance of significant…
Understanding the interplay between ordered structures and substrate curvature is an interesting problem with versatile applications, including functionalization of charged supramolecular surfaces and modern microfluidic technologies. In…
We discuss shape profiles emerging in inhomogeneous growth of squeezed tissues. Two approaches are used simultaneously: i) conformal embedding of two-dimensional domain with hyperbolic metrics into the plane, and ii) a pure energetic…
We argue that the standard classification of isometric deformations into infinitesimal v.s. finite is inadequate for the study of compliant shell mechanisms. Indeed, many compliant shells, particularly ones that are periodically corrugated,…
In this paper we prove some geometric inequalities for closed surfaces in Euclidean three-space. Motivated by Gage's inequality for convex curves, we first verify that for convex surfaces the Willmore energy is bounded below by some…
A classical problem in elasticity theory involves an inhomogeneity embedded in a material of given stress and shear moduli. The inhomogeneity is a region of arbitrary shape whose stress and shear moduli differ from those of the surrounding…
We present a new method to identify and characterize the structure of the intracluster medium (ICM) in simulated galaxy clusters. The method uses the median of gas properties, such as density and pressure, which we show to be very robust to…
Many tissues take the form of thin sheets, being only a single cell thick, but millions of cells wide. These tissue sheets can bend and buckle in the third dimension. In this work, we investigated the growth and shrinkage of suspended and…
The conformational statistics of ring polymers in melts or dense solutions is strongly affected by their quenched microscopic topological state. The effect is particularly strong for non-concatenated unknotted rings, which are known to…
Concrete subjected to combined compressive stresses and temperature loading exhibits compressive strains, which are considerably greater than for concrete subjected to compressive stresses alone. This phenomenon is called transient thermal…
Creases are purposely introduced to thin structures for designing deployable origami, artistic geometries, and functional structures with tunable nonlinear mechanics. Modeling the mechanics of creased structures is challenging because…
In this paper we obtain a sharp height estimate concerning compact hypersurfaces immersed into warped product spaces with some constant higher order mean curvature, and whose boundary is contained into a slice. We apply these results to…
We investigated the effects of particle shape on shear thickening in densely packed suspensions. Rods of different aspect ratios and non-convex hooked rods were fabricated. Viscosity curves and normal stresses were measured using a…
Liquid crystal elastomers (LCEs) can undergo large reversible contractions along their nematic director upon heating or illumination. A spatially patterned director within a flat LCE sheet thus encodes a pattern of contraction on heating,…
Graphene, dubbed as a two-dimensional material represents the topological concept of "surface" embedded in a three-dimensional space. This regard enables to employ existing theories/tools in topology to understand different…
Traditional computational approaches in simulating crack propagation in perfectly brittle materials rely on the estimate of stress intensity factors along the rupture front. This proves highly challenging in 3D when the crack geometry…
We examine the buckling shape and critical compression of confined inhomogeneous composite sheets lying on a liquid foundation. The buckling modes are controlled by the bending stiffness of the sheet, the density of the substrate, and the…
Many densely packed suspensions and colloids exhibit a behavior known as Discontinuous Shear Thickening in which the shear stress jumps dramatically and reversibly as the shear rate is increased. We performed rheometry and video microscopy…