The MT-FEM Model for Predicting Young's Modulus of Graphene Composites with Complex Morphologies

To address the inaccuracy of the traditional Mori-Tanaka method in predicting the Young's modulus of graphene composites-caused by the mismatch between the assumed reinforcement shape (e.g., ellipsoidal) and the actual morphology of graphene (e.g., rectangular, oblate, wrinkled)-this paper proposes a coupled Mori-Tanaka and finite element method (MT-FEM). In this approach, the actual shape of graphene reinforcements (such as rectangular, oblate, or wrinkled forms) and their corresponding strain concentration factors are accurately obtained via finite element modeling, and then incorporated into the Mori-Tanaka framework to determine the composite Young's modulus. The compatibility between the MT-FEM and the conventional Mori-Tanaka method is first verified through numerical examples. Furthermore, predictions by the MT-FEM show excellent agreement with existing literature results for graphene composites, with a deviation of less than 5%, confirming the reliability of the proposed method. Finally, the MT-FEM is applied to systematically investigate the influence of three graphene morphologies-rectangular, oblate, and wrinkled-on the composite Young's modulus. Results indicate that oblate graphene yields the highest enhancement in Young's modulus. At a graphene volume fraction of 0.03, the Young's modulus of composites reinforced with oblate graphene reaches 4.195 GPa, which is 13.75% and 13.93% higher than those reinforced with wrinkled (3.688 GPa) and rectangular (3.682 GPa) graphene, respectively. This study provides quantitative insights and theoretical guidance for the structural design and performance optimization of graphene-reinforced composites.