Nonlinear Constitutive Relations of Cellular Materials

The nonlinear constitutive relations of the cellular materials are presented in this paper based on the large deformation analysis of elastic beams in plane. The relations reflect the dependences of equivalent stress, equivalent Young's modulus, equivalent Poisson's ratio, and equivalent shear modulus on the deformation. It is found that the modified factors of the linear constitutive relations are associated with the shape and deformation of a considered cellular material and independent of the ratio of the face thickness t to length l (t/l) of the material. So the constitutive relations can describe the mechanical properties of the cellular materials with the same shape.