Level-set topology optimization for mechanical metamaterials under hybrid uncertainties

This paper proposes a level set-based robust topology optimization (RTO) method for computational design of metamaterials under hybrid uncertainties, e.g. auxetics with negative Poisson's ratio, where the Young's modulus of the solid is described as a random variable while the Poisson's ratio is regarded as an interval variable. Firstly, the robust objective function is formulated by a combination of interval mean and interval variance of the deterministic objective function. Secondly, the interval mean and interval variance are computed by a hybrid uncertain analysis approach, termed as Polynomial Chaos-Chebyshev Interval (PCCI) method. Thirdly, the design sensitivities of the robust objective function are obtained after the implementation of the PCCI method. Finally, a powerful parametric level set method (PLSM) in conjunction with the numerical homogenization method is applied to achieve the robust topological design for the auxetic microstructure. Several numerical cases are used to demonstrate the effectiveness of the proposed method for the robust topology optimization problems. This method is non-intrusive and general, and can be easily extended to a range of design problems of micro-structured metamaterials.