Maximum Stresses in Rectangular Auxetic Membranes

Auxetic materials exhibit a negative Poisson's ratio. Herein, the performance of rectangular auxetic membranes, under uniform load, is evaluated in terms of the maximum stress encountered. To facilitate convenient calculation, empirical modeling is conducted on the exact solution to reproduce displacement coefficients that are sufficiently accurate. A dimensionless maximum stress is then introduced to allow the effect from the membrane's Poisson's ratio and aspect ratio to be directly observed. Results reveal that 1) the dimensionless maximum stress reduces monotonically and nonmonotonically for conventional and auxetic membranes, respectively, 2) for the same Poisson's ratio magnitude the stresses in auxetic membranes are lower than those from conventional ones, 3) the optimal Poisson's ratio, on the basis of dimensionless maximum stress minimization, falls within the negative range, and 4) the dimensionless maximum stress minimization is especially effective for square membranes as well as very long and narrow membranes. It is therefore recommended that material auxeticity be taken into account-alongside geometrical and other material properties-in designing membranes and highly compliant very thin plates.