Metamaterials with Poisson’s ratio sign toggling by means of microstructural duality

Abstract

Neither positive nor negative Poisson's ratio materials are fully advantageous across a wide range of load bearing applications. In some cases, it is advantageous for structures to possess duality in material properties so as to take advantage of auxetic behavior under one loading condition as well as conventional behavior when the loading condition changes. This paper proposes two metamaterials-the hybrid rhombic-re-entrant metamaterial and the hybrid kite-arrowhead metamaterial-in which the prescription of either compressive or tensile load always leads to lateral expansion. Specifically, the Poisson's ratio of these metamaterials range from negative infinity to zero upon tensile load, and from zero to positive infinity upon compressive load. This duality of auxetic and conventional behavior for each of these metamaterial is achieved by employing a simultaneous lock and slide mechanism that is interchangeable upon load reversal. When loaded in one direction, the locked part takes effect while the sliding part becomes redundant. Upon load direction reversal, the previously locked and sliding parts convert to sliding and locked parts, respectively, thereby activating the redundant part while deactivating the functional part. The change in effective microstructural components, therefore, facilitates Poisson's ratio sign toggling with load reversal. Due to the indiscriminate lateral expansion regardless of the axial loading direction, such behavior in a fiber is useful to resist both fiber pull-out as well as fiber push-out from the matrix material.

A 2D auxetikos system based on interconnected shurikens

“…Perusal to Eqs. (18) and (19) indicates that both expressions are simplified when l c /l r = 1. If this rod ratio is selected as the central value, then the choice of 0.5 ≤ l c /l r ≤ 1.5 would be reasonable, and an increment of 0.25 would again give five sets of data.…”

“…In other words, It is therefore unsurprising that behavior of this network with different material and geometrical properties, one may perform calculations based on Eqs. (18) and (19) for heating and cooling, respectively, subjected to the following conditions to prevent the overlapping of neighboring shurikens or any other geometrical inconsistencies:…”

“…the radial dimension tends to increase regardless of whether the fiber is being pulled or being pushed, so as to prevent being displaced axially. By means of microstructural duality, each microstructure can be made to manifest two distinct effective microstructures such that v xy < 0 when σ xx > 0, but the Poisson's ratio sign toggles to v xy > 0 when σ xx < 0, thereby always giving ε yy > 0 regardless of whether σ xx is tensile or compressive [19], i.e. the dimension that is lateral to the stress application tends to increase, thereby indicating auxetikos behavior transverse to the load line.…”

Composite metamaterial square grids with sign-flipping expansion coefficients leading to a type of Islamic design

“…(3) whereby V = L 3 and dV = 3L 2 dL , substituting dV ∕V = 3dL∕L = 3 P into Eq. (42) gives which, upon comparison with Eq. (4), gives…”

“…For this reason, a series of metamaterials in which their effective material properties can switch between positive and negative signs have been introduced. These include the change in the Poisson's ratio sign upon reversal of stress direction [41,42], the change in the coefficient of thermal expansion sign upon temperature fluctuation [43,44], the change in Poisson's ratio sign with temperature fluctuations [45,46], and negative Poisson's ratio metamaterial with sign-switching expansion coefficients with environmental fluctuations [47,48].…”