Negative Poisson's ratio behavior induced by an elastic instability.

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. There is significant interest in the development of auxetic materials because of tremendous potential in applications in areas such as the design of novel fasteners, prostheses, piezocomposites with optimal performance and foams with superior damping and acoustic properties. The results of many investigations 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, natural layered ceramics, ferroelectric polycrystalline ceramics, and zeolites 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, hierarchical laminates, polymeric and metallic foams, microporous polymers, molecular networks, and many-body systems with isotropic pair interactions. Negative Poisson’s ratio effects have also been demonstrated at the micrometer scale using complex materials which were fabricated using soft lithography and at the nanoscale with sheets assemblies of carbon nanotubes. 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 been a bottleneck in the practical development towards applications. A structure which forms the basis of many auxetic materials is that of a cellular solid and research into the deformation these materials is a relatively mature field with primary emphasis on the role of buckling phenomena on load carrying capacity and energy absorption under compressive loading. Very recently, the results of a combined experimental and numerical investigation demonstrated that mechanical instabilities in 2D periodic porous structures can trigger dramatic transformations of the original geometry. Specifically, uniaxial loading of a square array of circular holes in an elastomeric matrix is found to lead to a pattern of alternating mutually orthogonal ellipses. This results from an elastic instability above a critical value of the applied strain. The geometric reorganization observed at the instability is both reversible and repeatable and it occurs over a narrow range of the applied load. Thus, this behavior provides opportunities for transformative materials with properties that can be reversibly switched. Similar instability induced pattern transformations have been observed also at the sub-micrometer scale. These observations pave the way for the development of a new class of materials which take advantage of such behavior. Here we exploit elastic instabilities to create novel effects within materials with periodic microstructure. We show that the pattern transformation leads to unidirectional negative Poisson’s ratio behavior for the 2D structure, i.e., it only occurs under compression. The uncomplicated manufacturing process of the samples together with the robustness of the observed phenomena suggests that this may form the basis of a practical method for constructing planar auxetic materials over a wide range of length-scales. Excellent quantitative agreement is found between numerical and experimental results to illustrate the effect for a specific sample. The numerical approach is subsequently used to explore the effect of void fraction and we uncover a scaling law for the phenomenon. Finally, we draw some conclusions and give future perspectives for this simple yet novel auxetic material. Our system comprised a square lattice of circular holes in an elastomeric matrix which was subjected to uniaxial compression using an Instron machine as described in the Experimental Section. A representative sequence of images of the sample during loading is presented in Figure 1, where the image shown in Figure 1a corresponds to the undeformed sample, prior to loading. During the initial response of the periodic structure, the circular holes were observed to undergo a gradual and homogeneous compression and this corresponds to a linearly C O M M U N IC A IO N www.advmat.de