Genetic programming-assisted micromechanical models of graphene origami-enabled metal metamaterials

Graphene origami (GOri) enabled metallic metamaterials are novel nanomaterials simultaneously possessing negative Poisson's ratio (NPR) and enhanced mechanical properties that are independent of the topology/architecture of the structure. Predicting their material properties via existing micromechanical models, however, is a great challenge. In this paper, a highly efficient micromechanical modeling approach based on molecular dynamics (MD) simulation and genetic programming (GP) algorithm is developed to address this key issue. The GP-based Halpin-Tsai model is extensively trained from MD simulation data to accurately predict the Young's modulus of GOri/Cu metamaterials with various GOri folding degrees, graphene contents and temperatures with a high coefficient of determination (R2) of ∼0.95. Meanwhile, the well-trained GP-based rule of mixture can accurately predict the coefficient of thermal expansion (CTE), Poisson's ratio and density of metamaterials with R2 of ∼0.95, ∼0.93 and ∼0.99, respectively. The excellent agreement between our estimated results and experimental data shows that the models developed herein are highly efficient and accurate in predicting mechanical properties that are essential for the analysis and design of functionally graded metal metamaterial composite structures. The theoretical results demonstrate that the proposed functionally graded metamaterial beam achieves significantly improved bending performance.