Journal of Theoretical
and Applied Mechanics

47, 4, pp. 737-750, Warsaw 2009

Micromechanical model of auxetic cellular materials

Małgorzata Janus-Michalska
An effective anisotropic continuum formulation for auxetic cellular materials is the objective of this paper. A skeleton is modelled as a plane beam elastic structure with stiff joints. The skeleton topology, forming concave polygons, is responsible for negative Poisson's ratio effect. The essential macroscopic features of mechanical behaviour are inferred from the deformation response of a representative volume element using the framework of micromechanical analysis. The strain energy of a unit cell is calculated by adding the tensile, shearing and bending strain energy of individual members. The equivalent continuum is based on averaging this energy, thus formulating the basis for computing the anisotropic stiffness matrix. The structural mechanics methodology and ANSYS finite element code are applied to solve the beam model of the skeleton. Graphical representation of certain material constants such as Young's modulus, Poisson's ratio, shear modulus and generalized bulk modulus is given. The results of included parametric study may be used for proper choice of geometric and material data of the skeleton for a given structural application of the anisotropic continuum.
Keywords: auxetic cellular materials; anisotropy; effective model; elasticity