Nonlinear Analysis of the In-Plane Young’s Moduli of Two-Dimensional Cellular Materials with Negative Poisson’s Ratios

This study deals with the in-plane Young’s moduli of two-dimensional auxetic cellular materials with negative Poisson’s ratios. The in-plane Young’s moduli of these cellular materials are theoretically analyzed, and calculated from the cell member bending with large deflection. Expressions for the in-plane Young’s moduli of the above-mentioned cellular materials are given by incomplete elliptic integrals. It is found that the in-plane Young’s moduli of two-dimensional cellular materials with negative Poisson’s ratios depend both on the geometry of the cell, and on the induced strain of these cellular materials. The in-plane Young’s moduli are no longer constants at large deformation. But at the limit of small strain, they converge to the results predicted by the small deformation model of flexure.