NEGATIVE AND CONVENTIONAL POISSONS RATIOS OF POLYMERIC NETWORKS WITH SPECIAL MICROSTRUCTURES

A theoretical model for evaluating effective Poisson's ratios of polymeric networks with special microstructures has been developed, which takes into account both stretching and bending deformation mechanisms. It is a complete generalization of the formalism first presented by Warren and Kraynik [Mech. Mater. 6, 27 (1987) and J. Appl. Mech. 55, 341 (1988)] for analytically calculating effective elastic properties of certain types of polymeric foams. Structural anisotropy in two special microstructures considered is found to have very significant effects on both magnitude and sign of the effective Poisson's ratios of the macroscopically isotropic network materials containing them. As two limiting cases, the effective Poisson's ratios of random assemblies of 2D and 3D bars or rods are shown to be 1/3 and 1/4, respectively, the latter of which recovers the well-known Poisson's result.