Modelling of auxetic structures

Abstract

Auxetic materials, i.e. those with negative Poisson's ratio, exhibit the unusual property of getting wider when stretched and thinner when compressed. Such materials are becoming very popular because of this unusual property. In this dissertation, we consider the egg rack, a periodic, three dimensional truss-like structure with auxetic properties. A unit cell of the egg-rack contains four ribs joined together at one end, with their other ends disposed as the vertices of a square. Linear elastic modelling was performed on the egg-rack with the help of the commercial code ANSYS® Academic Research v.12. A unit cell of the egg-rack was modelled using 30 beam elements. The loading conditions included both on axis compression, and shearing forces. Periodic boundary conditions were used to model the loading, taking advantage of the geometry's cyclic symmetry. Following these analyses, analytical models utilising the mechanism of beam flexure were set up to predict the in-plane mechanical properties in terms of the geometric and material properties of the constituent beams in the unit cell. An improved model was also proposed, were stretching, apart from flexing, was taken into consideration. Using 30 FE models, it was confirmed that the structure has a negative Poisson ratio in one direction, and a positive one in the other two original directions. It was also evident that flexing of the ribs was a predominant deformation mechanism. To a first approximation, the deformation of the beam model was very similar to the corresponding deformations of the 30-models under similar loading. For this reason, the analytical beam model was derived under the assumption of flexure alone. This model was sufficient to predict the in-plane Poisson ratio for most geometrical configurations. However, stretching becomes an important method of deformation as the egg-rack becomes flatter. The improved flexing and stretching beam model matched almost perfectly for all geometries. It was found that the on-axis Poisson ratio was always negative and almost constant at -1 when the beam lengths were equal. Furthermore, plots of Young's and shear moduli show that when the axial beams are inclined at 10° to 15°with the plane containing the on-axis compressive loads, the egg-rack will have relatively high elastic moduli and small Poisson's ratio. Plots of the off-axis Poisson ratio were also included, this information being useful for the design of materials with tailor-made mechanical properties.