Numerical Analysis of Dynamic Properties of an Auxetic Structure with Rotating Squares with Holes

Abstract

In this paper, a novel auxetic structure with rotating squares with holes is investigated. The unit cell of the structure consists of four units in the shape of a square with cut corners and holes. Finally, the structure represents a kind of modified auxetic structure made of rotating squares with holes or sheets of material with regularly arranged diamond and square cuts. Effective and dynamic properties of these structures depend on geometrical properties of the structure. The structures are characterized by an effective Poisson’s ratio from negative to positive values (from about minus one to about plus one). Numerical analysis is made for different geometrical features of the unit cells. The simulations enabled the determination of the dynamic characteristic of the analyzed structures using vibration transmission loss, transmissibility, and mechanical impedance. Numerical calculations were conducted using the finite element method. In the analyzed cases of cellular auxetic structures, a linear elasticity model of the material is assumed. The dynamic characteristic of modified rotating square structures is strongly dependent not only on frequency. The dynamic behavior could also be enhanced by adjusting the geometric parameter of the structure. Auxetic and non-auxetic structures show different static and dynamic properties. The dynamic properties of the analyzed structures were examined in order to determine the frequency ranges of dynamic loads for which the values of mechanical impedance and transmissibility are appropriate.

A finite element analysis of auxetic composite fabric with rotating square structure

“…In their mathematical model, the Poisson's ratio of this structure was a constant of À1 if the square units were perfectly rigid and did not deform upon loading. This system still stands even if the square unit is replaced by other designs, such as a rigid cross/triangle/parallelogram, hierarchical ensemble, or a frame with non-space filling [31][32][33] During the exploitation process of the rotating square structure, it should be noticed that it is almost impossible to produce a material with ideal rigidity. To reveal the importance of the rigidity of the square unit, Grima et al developed a model with semi-rigid squares by adding an additional degree of freedom.…”

Design of hierarchical microstructures with isotropic elastic stiffness

“…For instance, various classes of auxetic HMs have been designed by achieving the hierarchy either in each level of cells or in the whole microstructures [37]. The HMs can have either honeycomb-like geometries [38], re-entrant-type configurations [39] or rotating units [40]. These auxetic HMs can gain enhanced mechanical characteristics, including the high shear stiffness, fracture toughness among others [40][41][42][43].…”

“…The HMs can have either honeycomb-like geometries [38], re-entrant-type configurations [39] or rotating units [40]. These auxetic HMs can gain enhanced mechanical characteristics, including the high shear stiffness, fracture toughness among others [40][41][42][43]. Furthermore, many other HMs have been designed for realizing high resistance to brittle failure [44,45], high strength [29,34,35], and superior energy absorption capabilities [46].…”

Metamaterials with Poisson's ratio discontinuity by means of fragmentation–reconstitution rotating units

“…A wide range of structural two- and three-dimensional models with negative Poisson's ratio explain auxeticity. Such structures include the well-known honeycombs (such as the re-entrant or concave hexagonal), chiral, anti-chiral, rotating rigid units (squares, rectangles and triangles), liquid crystalline polymers, dilating triangles, egg rack structures, sinusoidal ligaments, metamaterials, hard discs [21] or periodic microstructures such as a square array of holes in a matrix or rotating units with holes [22], and other systems. Analogies across auxetic models based on deformation mechanisms have been earlier described [23].…”

“…The dynamic behaviour of auxetic material could also be enhanced by adjusting the geometric parameter of the structure. Auxetic and non-auxetic structures show different static and dynamic properties [22]. The authors examined the dynamic properties of the analysed structures (rotating units with holes which generate positive and negative Poisson's ratio) to determine the frequency ranges of dynamic loads for which the values of mechanical impedance and transmissibility are appropriate.…”