Negative Poisson's Ratio Behavior Induced by an Elastic Instability

Abstract

When materials are compressed along a particular axis they are most commonly observed to expand in directions orthogonal to the applied load. The property that characterizes this behavior is the Poisson's ratio which is defined as the ratio between the negative transverse and longitudinal strains. The majority of materials are characterized by a positive Poisson's ratio which is approximately 0.5 for rubber and 0.3 for glass and steel. Materials with a negative Poisson's ratio will contract (expand) in the transverse direction when compressed (stretched) and, although they can exist in principle, demonstration of practical examples is relatively recent. Discovery and development of materials with negative Poisson's ratio, also called auxetics, was first reported in the seminal work of Lakes in 1987. [1] There is significant interest in the development of auxetic materials because of tremendous potential in applications in areas such the design of novel fasteners [2] , prostheses [3] , piezocomposites with optimal performance [4] and foams with superior damping and acoustic properties [5] . The results of many investigations [6][7] suggest that the auxetic behavior involves an interplay between the microstructure of the material and its deformation. Examples of this are provided by the discovery that metals with a cubic lattice [8] , natural layered ceramics [9] , ferroelectric polycrystalline ceramics [10] and zeolites [11] may all exhibit negative Poisson's ratio behavior. Moreover, several geometries and mechanisms have been proposed to achieve negative values for the Poisson's ratio, including foams with reentrant structures [1] , hierarchical laminates [12] , polymeric and metallic foams [13] , microporous polymers [14] , molecular networks [15] and manybody systems with isotropic pair interactions [16] . Negative Poisson's ratio effects have also been demonstrated at the micron scale using complex materials which were fabricated using soft lithography [17] and at the nanoscale with sheets assemblies of carbon nanotubes [18] .A significant challenge in the fabrication of materials with auxetic properties is that it usually involves embedding structures with intricate geometries within a host matrix. As such, the manufacturing process has

Compaction Through Buckling in 2D Periodic, Soft and Porous Structures: Effect of Pore Shape

“…2A). This behavior has been demonstrated to provide opportunities for the design of materials with tunable negative Poisson's ratio [17], phonic switches [18] and strain-tunable optomechanical materials [19]. However, so far only the response of structures with circular and elliptical holes has been investigated and the effect of the pores shape on the structural response has not been explored yet.…”

“…Since our results clearly show that the finite element simulations were able to accurately reproduce the experimental results, we now investigate numerically the response of structures characterized by porosity ϕ ranging between 0.4 and 0.5. Note that smaller values of porosity would facilitate macroscopic instability [17], leading to structures characterized by limited compaction. On the other hand, higher levels of porosity would lead to structures characterized by very thin ligaments, making them fragile.…”

Low Porosity Metallic Periodic Structures with Negative Poisson's Ratio

“…Using this technique, structures that exhibit negative Poisson's ratio have been designed [29,30] and the results indicate that to achieve optimal auxetic response in low porosity structures, the microstructure must comprise an array of mutually orthogonal, very elongated holes [31]. Interestingly, auxetic response has also been observed in elastomeric porous structures where a pattern of mutually orthogonal ellipses is induced by buckling [32].…”

A composite material with Poisson’s ratio tunable from positive to negative values: an experimental and numerical study

“…The current state of research for most NPR materials is still limited to a theoretical stage. Besides cellular solids and some fiber-reinforced composites, there are a few successful NPR materials that can be easily manufactured and employed in a real engineering environment [14,[27][28][29]. It is because most NPR materials usually have some embedded structures with intricate geometries.…”