Auxetic behaviour from rotating triangles : a generic model with special attention to auxetic foams

Abstract

Materials having a negative Poisson's ratio, more commonly known as auxetics, exhibit the unusual property of getting fatter rather than thinner when uniaxially stretched. This phenomenon has been often explained through models which describe how particular geometric features in the micro or nano structure of the material deform when subjected to uniaxial loads. Here, a new model based on scalene rigid triangles which rotate relative to each other will be presented and analysed. It is shown that this model can exhibit 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 densification properties. This system has various applications which include the design of the underlying geometry of auxetic filters and perforated sheets. Furthermore, special cases of such generic structure in particular isotropic auxetic structures will be considered. One such special case is adapted to represent open cell foams so as to analyse their behaviour upon loading using finite element simulations. The deformation of the structure, in particular the changes in its parameters through analytical modelling and finite element simulations is discussed.