Auxetic Structures from Rotating Squares (original) (raw)
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Investigation of Modified Auxetic Structures from Rigid Rotating Squares
Materials
Auxetic structures exhibit unusual changes in size, expanding laterally upon stretching instead of contracting. This paper presents this effect in a failsafe mode in structures made of rigid squares. We applied the concept of auxetic structures made of rigid rotating squares (from Grima and Evans) and offer a novel solution for connecting them. By introducing axes of rotation on the surface of the squares, a reliable working system is obtained, free from stress, in which the squares can come into contact with each other and completely cover the surface of the structure, or, in the open position, form regularly arranged pores. Herein, we present a new 2D auxetic metamaterial that is mathematically generated based on a theoretical relationship of the angle between the edges of a square and the position of the axis of rotation. Physical models were generated in the form of a planar structure and in the form of a circular closed structure. Such physical models confirmed our initial cons...
Auxetic Behaviour of Rigid Connected Squares
Materials
The paper presents an analysis of rotating rigid unit (RRU) auxetic structures, the special property of which is negative Poisson’s ratio. The crucial features of such modified structures are the well-functioning linkages of the square units at their pivot points. This ensures the stable functioning of such structures in tension or compression. The presented geometrical analysis of these auxetic structures may facilitate their adequate construction and allow one to determine the expected values of their expansion as well as the desired porosity. The results are confirmed based on the behaviour of physical models produced by the assembly of square units. The change in the dimensions of the physical models when moving from a closed to an open position is consistent with the predictions of the geometric models. By modifying the well-known ‘rotating squares’ model, physical structures with auxetic properties are obtained that can be utilised in industrial conditions, where a simultaneou...
On the auxetic properties of rotating rhombi and parallelograms: A preliminary investigation
Physica Status Solidi B-basic Solid State Physics, 2008
Auxetics exhibit the unusual property of expanding when uniaxially stretched (negative Poisson's ratio), a property that is usually linked to particular geometric features and deformation mechanisms. One of the mechanisms which results in auxetic behaviour is the one involving rotating rigid units, for which, systems made from triangles, squares or rectangles have already been considered. In this work we extend this study by considering systems which can be constructed from either connected rhombi or connected parallelograms. We show that various types of such systems can exist and we discuss in detail the properties of one type of ‘rotating rhombi' and one type of ‘rotating parallelograms'. We also show that the Poisson's ratio of these systems, which can be positive or negative, is anisotropic and dependent on the shape of the parallelograms/rhombi and the degree of openness of the system. (© 2008 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)
Numerical Analysis of Dynamic Properties of an Auxetic Structure with Rotating Squares with Holes
Materials
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 struc...
Planar isotropic structures with negative Poisson’s ratio
International Journal of Solids and Structures, 2012
A new design principle is suggested for constructing auxetic structures-the structures that exhibit negative Poisson's ratio (NPR) at macroscopic level. We propose 2D assemblies of identical units made of a flexible frame with a sufficiently rigid reinforcing core at the centre. The core increases the frame resistance to the tangential movement thus ensuring high shear stiffness, whereas the normal stiffness is low being controlled by the local bending response of the frame. The structures considered have hexagonal symmetry, which delivers macroscopically isotropic elastic properties in the plane perpendicular to the axis of the symmetry. We determine the macroscopic Poisson's ratio as a ratio of corresponding relative displacements computed using the direct microstructural approach. It is demonstrated that the proposed design can produce a macroscopically isotropic system with NPR close to the lower bound of À1. We also developed a 2D elastic Cosserat continuum model, which represents the microstructure as a regular assembly of rigid particles connected by elastic springs. The comparison of values of NPRs computed using both structural models and the continuum approach shows that the continuum model gives a healthy balance between the simplicity and accuracy and can be used as a simple tool for design of auxetics.
2021
1M. Tech-Mechanical Engineering (Design) Student, Vishwakarma Institute of Technology, Pune, India. 2Professor, Department of Mechanical Engineering, Vishwakarma Institute of Technology, Pune, India. -------------------------------------------------------------------------***-----------------------------------------------------------------Abstract – Auxetic structures are class of nonconventional structures having negative Poisson’s ratio. They expand laterally when axially stretched and laterally contract when axially compressed which is different from conventional structures. Light weight, high strength, impact damping capabilities and stiffness offers potential applications in the field of aerospace, automobile, military protection equipment, textile, suspension mount. Although different auxetic structures are studied and analyzed because of their strength to weight ratio and negative Poisson’s ratio, there is need of development of new structures to improve these properties. The...
Gazi Üniversitesi Fen Bilimleri Dergisi Part C: Tasarım ve Teknoloji
Poisson’s ratio, one of the important mechanical properties of materials and structures, is positive for almost all of the known materials and structures. However, auxetic materials or structures has negative Poisson’s ratios. Characteristics of the auxetic structures are very important to be used in design of a new structure. Computational or experimental studies on auxetic structures have been increasing in literature. In this study, a new auxetic lattice structure with different Poisson’s ratios was designed and studied by finite element analysis. Mechanical properties of the newly designed auxetic lattice structures were analyzed with different lattice inner thickness. Results showed that change in inner thickness affects the Poisson’s ratio, mass, volume and surface area of the newly designed Auxetic lattice structures.
Negative Poisson's Ratios from Rotating Rectangles
Computational Methods in Science and Technology, 2004
Materials with a negative Poisson's ratio exhibit the unexpected property of becoming fatter when stretched and narrower when compressed. This counter-intuitive behaviour is known as 'auxetic behaviour' and imparts many beneficial effects on the material's macroscopic properties. This paper discusses the potential of systems composed of rigid rectangles connected together through flexible hinges at their vertices. It will be shown that, on application of uniaxial loads, these rigid rectangles will rotate with respect to each other to form, in some cases, a more open structure hence giving rise to a negative Poisson's ratio.
IRJET, 2021
Auxetic structures are class of nonconventional structures having negative Poisson's ratio. They expand laterally when axially stretched and laterally contract when axially compressed which is different from conventional structures. Light weight, high strength, impact damping capabilities and stiffness offers potential applications in the field of aerospace, automobile, military protection equipment, textile, suspension mount. Although different auxetic structures are studied and analyzed because of their strength to weight ratio and negative Poisson's ratio, there is need of development of new structures to improve these properties. The present work is focused on design of arrowhead shaped auxetic structure and to explore influence of the geometrical parameters of arrowhead shaped auxetic structure on negative Poisson's ratio. In this work, the equation of Poisson's ratio for arrowhead shaped structure is derived. By changing the values of angle , wall thickness and length of small wall of unit cell; the value of Poisson's ratio is analytically determined and it is verified with Finite Element Analysis. It is concluded that Poisson's ratio of arrowhead shaped structure is a function of angle , wall thickness and length of small wall of unit cell. Here the angle plays a major role.
On the auxetic properties of generic rotating rigid triangles
2012
Materials having a negative Poisson's ratio (auxetic) get fatter rather than thinner when uniaxially stretched. This phenomenon has been often explained through models that describe how particular geometric features in the micro or nanostructure of the material deform when subjected to uniaxial loads. Here, a new model based on scalene rigid triangles rotate relative to each other will be presented and analysed. It is shown that this model can afford a very wide range of Poisson's ratio values, the sign and magnitude of which depends on the shape of the triangles and the angles between them. This new model has the advantage that it is very generic and may be potentially used to describe the properties in various types of materials, including auxetic foams and their relative surface density. Specific applications of this model, such as a blueprint for a system that can exhibit temperature-dependent Poisson's ratios, are also discussed.