Robust topology optimization of negative Poisson’s ratio metamaterials under material uncertainty

Abstract

Metamaterials are synthetic materials designed to have unique properties like negative Poisson ratio (NPR). NPR metamaterials, also known as auxetics, offer significant value in applications that require high energy absorption, e.g., packing materials, medical knee pads, footwear. However, material uncertainty arising out of manufacturing tolerance, inhomogeneity of material properties, and others could lead to significant variations in the response of the metamaterials. Thus, a SIMP based robust topology optimization (RTO) design for the NPR metamaterials under material uncertainty is investigated. The weighted mean and variance of the deterministic objective function is utilized to form a robust objective function. The variation in effective Poisson’s ratio with respect to the lower bound goes from 15.40% to 105% with deterministic topology optimization. In contrast, RTO produces more stable designs and shows the variation of only 1.72% to 2.54%. Several parametric studies are used to demonstrate the feasibility of the proposed RTO methodology.