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.

超材料是合成材料，旨在具有独特的特性，如负泊松比 (NPR)。NPR 超材料，也称为拉胀材料，在需要高能量吸收的应用中具有重要价值，例如包装材料、医用护膝、鞋类。然而，由制造公差、材料特性的不均匀性等引起的材料不确定性可能导致超材料响应的显着变化。因此，研究了在材料不确定性下用于 NPR 超材料的基于 SIMP 的稳健拓扑优化 (RTO) 设计。利用确定性目标函数的加权均值和方差来形成稳健的目标函数。有效泊松比相对于下限的变化从 15 开始。40% 到 105% 使用确定性拓扑优化。相比之下，RTO 产生更稳定的设计并且显示的变化仅为 1.72% 到 2.54%。几个参数研究被用来证明所提议的 RTO 方法的可行性。