Effect of auxetic behavior on effective properties of composite materials

In this paper, a two–phase composite material consisting of negative Poisson's ratio elastic material is considered. The effective elastic properties (bulk modulus, shear modulus and Poisson's ratio) of two–dimensional heterogeneous materials are estimated by the finite element numerical homogenization technique. To this end, three constructs were used to investigate the effect of auxetic behavior on effective properties. The matrix of the first structure has auxetic behavior, Negative Poisson's Ratio NPR, the circular inclusions are elastic with Positive Poisson's Ratio PPR. The inclusions of another structure are circular auxetic material, the matrix is elastic material. The last case is that both matrix and inclusions possess auxetic property. And taking into account five different volume fractions from each case. The concept of Representative Volume Element RVE is introduced, in which the homogenization numerical simulation based on finite element is carried out. The effectiveness of numerical calculation is verified by applying two boundary, periodic boundary conditions and kinematic uniform boundary conditions. We demonstrate that by mixing auxetic and non–auxetic phases into composites, it is possible to preserve some of the unique properties of auxetic materials while enhancing the unique properties of traditional single–phase materials. The strengthening effect is controlled by Poisson's ratio of each phase, elastic modulus, and shape of inclusions. Studying the strengthening effect of composite auxetic materials can provide a reference for designing composite materials with new properties.