相关论文: Neutral Deformation Modes of Minimal Surfaces

Minimal surfaces are ubiquitous in nature. Here they are considered as geometric objects that bear a deformation content. By refining the resolution of the surface deformation gradient afforded by the polar decomposition theorem, we…

Three general modes are distinguished in the deformation of a thin shell; these are stretching, drilling, and bending. Of these, the drilling mode is the one more likely to emerge in a soft matter shell (as compared to a hard, structural…

In the direct approach to continua in reduced space dimensions, a thin shell is described as a mathematical surface in three-dimensional space. An exploratory kinematic study of such surfaces could be very valuable, especially if conducted…

Many compliant shell mechanisms are periodically corrugated or creased. Being thin, their preferred deformation modes are inextensional, i.e., isometric. Here, we report on a recent characterization of the isometric deformations of periodic…

A shape sensitive, variational approach for the matching of surfaces considered as thin elastic shells is investigated. The elasticity functional to be minimized takes into account two different types of nonlinear energies: a membrane…

A periodic surface is one that is invariant by a 2D lattice of translations. Deformation modes that stretch the lattice without stretching the surface are effective membrane modes. Deformation modes that bend the lattice without stretching…

We propose a model for nonlinearly elastic membranes undergoing finite deformations while confined to a regular frictionless surface in $\mathbb{R}^3$. This is a physically correct model of the analogy sometimes given to motivate harmonic…

I consider the shape of a deformed elastic shell. Using the fact that the lowest-energy, small deformations are along infinitesimal isometries of the shell's mid-surface, I describe a class of weakly-stretching deformations for thin shells…

Mode surfaces are the generalization of degenerate curves and neutral surfaces, which constitute 3D symmetric tensor field topology. Efficient analysis and visualization of mode surfaces can provide additional insight into not only…

When subjected to specific prestresses, continuum elastic shells can exhibit geometric zero modes: complex motions that require vanishing elastic energy to excite, enabling them to be driven by weak and generic energy inputs. Despite recent…

We investigate a minimal model of the plastic deformation of amorphous materials. The material elements are assumed to exhibit ideally plastic behavior (J2 plasticity). Structural disorder is considered in terms of random variations of the…

We consider the problem of distortion minimal morphing of $n$-dimensional compact connected oriented smooth manifolds without boundary embedded in $\R^{n+1}$. Distortion involves bending and stretching. In this paper, minimal distortion…

We study the lubrication of fluid-immersed soft interfaces and show that elastic deformation couples tangential and normal forces and thus generates lift. We consider materials that deform easily, due to either geometry (e.g. a shell) or…

There are three fundamental physical processes that gives rise to the morphology of a surface: deposition, surface diffusion and desorption. The characteristics of the interfaces generated by the combination of deposition and surface…

An optimal microswimmer with a given geometry has a surface velocity profile that minimizes energy dissipation for a given swimming speed. An axisymmetric swimmer can be puller-, pusher-, or neutral-type depending on the sign of the…

We show that two-dimensional systems of deformable particles undergo a continuous liquid-hexatic transition upon compression or cooling, but no hexatic-solid transition-even at zero temperature and high density. Numerical simulations reveal…

We found a class of triangulated surfaces in Euclidean space which have similar properties as isothermic surfaces in Differential Geometry. We call a surface isothermic if it admits an infinitesimal isometric deformation preserving the mean…

Plates generally admit six deformation modes: three of which are high in strain energy, stretch the plate's midsurface and are called membrane modes; and three are low-energy, bend the midsurface without stretching it and are called bending…

We propose bending energies for isotropic elastic plates and shells. For a plate, we define and employ a surface tensor that symmetrically couples stretch and curvature such that any elastic energy density constructed from its invariants is…

Thin surfaces are ubiquitous in nature, from leaves to cell membranes, and in technology, from paper to corrugated containers. Structural thinness imbues them with flexibility, the ability to easily bend under light loads, even as their…