Related papers: Wallpaper Groups and Auxetic Metamaterials
Negative Poisson's ratio (NPR) materials have drawn significant interest because the enhanced toughness, shear resistance and vibration absorption that typically are seen in auxetic materials may enable a range of novel applications. In…
This paper focuses on the conditions for obtaining auxetic, i.e. with a negative Poisson's ratio, composite laminates made of specially orthotropic layers. In particular, the layers considered are of three types: R1-orthotropic, i.e.…
Recent advances in nanoscale fabrication enable atomic-scale manipulation of two-dimensional (2D) materials by introducing engineered pores and perforations. This provides new opportunities to tailor functional properties of 2D materials…
A long-standing question is why Poisson's ratio v nearly always exceeds 0.2 for isotropic materials, whereas classical elasticity predicts v to be between -1 to 1/2. We show that the roots of quadratic relations from classical elasticity…
In this work, we conduct a systematic study of Hamiltonian and quasi-Hamiltonian systems within the framework of nondecomposable generalized Poisson geometry. Our focus lies on the interplay between the algebraic structure of…
"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…
Odd transport phenomena -- defined as a flux response orthogonal to an applied gradient -- have been recently observed in isotropic systems, with a multitude of proposed models and experiments to study these effects. Odd transport manifests…
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…
When randomly displacing the nodes of a crystalline and unstressed spring network, we find that the Possion's ratio decreases with the increase of structural disorder and even becomes negative. Employing our finding that longer springs tend…
This study is about the properties of the sets of objects associated in a structure resulting from multiple-processes involving chance as are materials whose texture is unordered and random. Being a paper scientist the author refers to the…
Poisson brackets provide the mathematical structure required to identify the reversible contribution to dynamic phenomena in nonequilibrium thermodynamics. This mathematical structure is deeply linked to Lie groups and their Lie algebras.…
We discuss a non-equilibrium statistical system on a graph or network. Identical particles are injected, interact with each other, traverse, and leave the graph in a stochastic manner described in terms of Poisson rates, possibly dependent…
This work is concerned with the micro-architecture of multi-layer material that globally exhibits desired mechanical properties, for instance a negative apparent Poisson ratio. We use inverse homogenization, the level set method, and the…
We describe the mathematical properties of pairwise comparisons matrices with coefficients in an arbitrary group. We provide a vocabulary adapted for the description of main algebraic properties of inconsistency maps, describe an example…
In this paper we investigate numerically an instance of the problem of G-closure for two-dimensional periodic metamaterials. Specifically, we consider composites with isotropic homogenized elasticity tensor, obtained as a mixture of two…
In computer graphics and engineering, nonlinear elastic material properties of 3D volumetric solids are typically adjusted by selecting a material family, such as St. Venant Kirchhoff, Linear Corotational, (Stable) Neo-Hookean, Ogden, etc.,…
To any finite ordered subset and any finite partition of a group a set of tuples of positive integers, named as configurations, is associated that describes the group's behavior. The present paper provides an exposition of this notion and…
Adhesion is a fundamental phenomenon that plays a role in many engineering and biological applications. This paper concerns the use of machine learning to characterize the effective adhesive properties when a thin film is peeled from a…
A family of Poisson structures, parametrised by an arbitrary odd periodic function $\phi$, is defined on the space $\cW$ of twisted polygons in $\RR^\nu$. Poisson reductions with respect to two Poisson group actions on $\cW$ are described.…
Silicon dioxide or silica, normally existing in various bulk crystalline and amorphous forms, is recently found to possess a two-dimensional structure. In this work, we use ab initio calculation and evolutionary algorithm to unveil three…