Topology optimisation for isotropic mechanical metamaterials considering material uncertainties

Abstract Isotropic materials are widely used because they retain their properties regardless of the measurement directions. However, their mechanical properties tend to deteriorate owing to disturbances in the base material parameters. This study, for the first time, systematically investigates multiple isotropic materials by considering material uncertainties with respect to the elastic modulus and Poisson's ratio. A smooth bi-directional evolutionary topology optimisation method, is employed to identify optimal topological configurations for material microstructures, macroscopic equivalent properties of the microstructures are evaluated via the comprehensible energy-based homogenisation method. A non-intrusive polynomial chaos expansion model is employed to implicitly quantify uncertainties in the base material subject to Gaussian distributions. Additionally, both the expectations and standard variations in extreme properties are considered as the objective function, and a measurement index is defined to determine whether the designed microstructures are isotropic. Lastly, the deterministic and uncertain cases for numerical examples are compared to demonstrate the efficiency of the proposed method.