Adaptive triangular-mesh coarse-grained model for notched 2D metamaterials: A hybrid FEA and top-down approach

Motivated by the demand of computational flexibility and efficiency, we present a novel approach for coarse-grained (CG) modeling of notched 2D metamaterials, highlighting a “top-down” strategy with adaptive triangular mesh and Morse bond potential. The proposed approach focuses on a typical 2D material of graphene with different circular notches as a case study. Particularly, based on the assumption of equivalent energy, a triangular mesh is adopted to map areas into triangles, which is optimized by using the covariance matrix adaptation evolution strategy (CMA-ES) algorithm to determine the best-fitting parameters of the Morse bond potential, for models with both uniform and non-uniform meshes. Instead of relying on theoretical calculations, an exponential relationship is formulated between the Morse bond potential parameters and the bond length. The numerical results show that the CMA-ES algorithm demonstrates excellent convergence for all bond lengths, with models taking approximately 20 generations to converge. Compared with conventional bottom-up coarse-grained modeling schemes, the proposed approach leads to much smoother boundaries around notches and displays decent adaptability in a variety of models. The results show that the proposed model is highly consistent with the full-atom model, and is proved to be effective in studying the mechanical properties of notched 2D metamaterials, paving the way for the design and development of advanced 2D metamaterials with inherent or prefabricated notches.