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 trian-gular 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 meta-materials, paving the way for the design and development of advanced 2D metamaterials with inherent or prefabricated notches.

Automated summary

Motivated by computational flexibility and efficiency, this paper presents a novel approach for coarse-grained modeling of notched 2D metamaterials. The approach utilizes an adaptive triangular mesh and Morse bond potential, optimized using the CMA-ES algorithm. The results demonstrate that the proposed approach provides smooth boundaries and good adaptability, and is effective in studying the mechanical properties of notched 2D metamaterials.