相关论文: Auxetic deformations and elliptic curves

We formulate a mathematical theory of auxetic behavior based on one-parameter deformations of periodic frameworks. Our approach is purely geometric, relies on the evolution of the periodicity lattice and works in any dimension. We…

Materials science has adopted the term of auxetic behavior for structural deformations where stretching in some direction entails lateral widening, rather than lateral shrinking. Most studies, in the last three decades, have explored…

In materials science, auxetic behavior refers to lateral widening upon stretching. We investigate the problem of finding domains of auxeticity in global deformation spaces of periodic frameworks. Case studies include planar periodic…

A symmetry-extended Maxwell treatment of the net mobility of periodic bar-and-joint frameworks is used to derive a sufficient condition for auxetic behaviour of a 2D material. The type of auxetic behaviour that can be detected by symmetry…

Framework materials and their deformations provide a compelling relation between materials science and algebraic geometry. Physical distance constraints within the material transform into polynomial constraints, making algebraic geometry…

Despite their outstanding mechanical properties, with many industrial applications, a rational and systematic design of new and controlled auxetic materials remains poorly developed. Here a unified framework is established to describe…

"Auxetic" materials have the counter-intuitive property of expanding rather than contracting perpendicular to an applied stretch, formally they have negative Poisson's Ratios (PRs).[1,2] This results in properties such as enhanced energy…

We show that, for any given dimension $d\geq 2$, the range of distinct possible designs for periodic frameworks with auxetic capabilities is infinite. We rely on a purely geometric approach to auxetic trajectories developed within our…

We present a three-periodic, chiral, tensegrity structure and demonstrate that it is auxetic. Our tensegrity structure is constructed using the chiral symmetry {\Pi}+ cylinder packing, transforming the cylinders themselves to the elastic…

Anisotropies of Young's modulus E, the shear modulus G, and Poisson's ratio of all 2D symmetry systems are studied. Simple necessary and sufficient conditions on their elastic compliances are derived to identify if any of these crystals are…

Detecting elliptical objects from an image is a central task in robot navigation and industrial diagnosis where the detection time is always a critical issue. Existing methods are hardly applicable to these real-time scenarios of limited…

We present an analytical model to investigate the mechanics of 2-dimensional lattices composed of elastic beams of non-uniform cross-section. Our approach is based on reducing a lattice to a single beam subject to the action of a set of…

We identify the restricted class of attainable effective deformations in a model of reinforced composites with parallel, long, and fully rigid fibers embedded in an elastic body. In mathematical terms, we characterize the weak limits of…

Discovering the physical requirements for meeting the indefinite permittivity in natural material as well as proposing a new natural hyperbolic media offer a possible route to significantly improve our knowledge and ability to confine and…

This paper is devoted to the exploration of rectangular finite elements' ability to model the stress-strain state of isotropic and orthotropic materials with a negative Poisson's ratio, known as auxetic materials. By employing linear…

Detecting structures at the particle scale within plastically deformed crystalline materials allows a better understanding of the occurring phenomena. While previous approaches mostly relied on applying hand-chosen criteria on different…

Mechanical couplings with symmetry breaking open up novel applications such as robotic metamaterials and directional mechanical signal guidance. However, most studies on 3D mechanical couplings have been limited to ad-hoc axial-twist…

We propose a class of auxetic three-dimensional lattice structures. The elastic microstructure can be designed in order to have omni-directional Poisson's ratio arbitrarily close to the stability limit -1. The cubic behavior of the periodic…

This paper designs an alogrithm to compute the minimal combinations of finite sets in Euclidean spaces, and applys the algorithm of study the moment maps and geometric invariant stability of hypersurfaces. The classical example of cubic…

Auxetic materials are a novel class of mechanical metamaterials which exhibit an interesting property of negative Poisson ratio by virtue of their architecture rather than composition. It has been well established that a wide range of…