Auxetic materials and structures are a novel class of materials, which have negative Poisson's ratio. Unlike conventional materials, these materials become thicker when applied under tensile stress perpendicular to the applied force and thinner when applied under compressive stress. These materials are composed of cellular units that are the usual auxetic effect caused by these cells and have different structures according to the diversity of cells. The elastic modulus and Poisson's ratio have a high impact and importance on the structure's displacement and strain. In this paper, the effect of the ratio of geometric parameters and porosity of the reentrant structure in a two-dimensional state by finite elements and analytical relations on the Poisson's ratio and elastic modulus were investigated. Then, the sensitivity analysis of each of the geometric parameters of the structure was performed by a statistical technique called SOBEL on the elastic modulus and Poisson's ratio. The achieved results indicate that angle has the most significant influence on the elastic modulus and the Poisson's ratio. Eventually, according to the obtained results, we model the reentrant structure so that it works under the stretch corresponding to the sample. This property of auxetic materials can be employed in the medical, sports, and robotics industries.
