An optimization strategy for customizable global elastic deformation of unit cell-based metamaterials with variable material section discretization

• Extended optimization framework with a material section discretization scheme. • Automated update of the material section discretization to improve convergence. • Material section discretization controlled by the gradient of geometric variables. • Optimization of unit cell parameter distribution in metamaterials. • Reduction of optimization time and variable gradients. Metamaterials with their distinctive unit cell-based periodic architecture feature a wide range of possible properties with unusual characteristics and a high potential for optimization. Due to their complex interaction between unit cell geometry and material properties, as well as their inherent multi-scale nature, suitable optimization strategies need to be developed for metamaterials. One potential approach is to optimize the distribution of unit cells within a part to achieve a predefined deformation response. However, a significant challenge lies in determining the appropriate number and distribution of areas with varying properties (material sections) to facilitate an efficient optimization. In this study, a variable material section discretization scheme is presented, which is aimed at automatically updating the discretization to enhance the efficiency of metamaterial optimizations. This scheme is implemented as an extension to a previously proposed Finite Element simulation-based optimization framework for unit cell-based metamaterials. The framework includes a numerical homogenization method and interpolation scheme for efficiently correlating unit cell parameters with homogenized material properties, coupled with a black-box optimization method. In the present study, the previously proposed framework was extended to incorporate a scheme for monitoring and adjusting the material section discretization during the optimization process. To assess the effectiveness of the implemented routine, it was tested in conjunction with a genetic algorithm for optimizing the parameter distribution of a 2D tri-anti-chiral metamaterial to match a predefined lateral deformation under load.