Mechanical modeling of graphene using the three-layer-mesh bridging domain method

Recently developed three-layer-mesh bridging domain method (TBDM) enhanced the conventional bridging domain method (BDM) by (1) mitigating the temperature cooling effect on the atoms in the bridging domain, and (2) employing a mesh-independent physics-based discrimination between thermal and mechanical atomic motions. In this paper, we present the new enhancements for the TBDM to achieve an appropriate framework for concurrently coupled atomistic-continuum simulation of graphene. To capture the mechanical behavior of graphene accurately, we employed the adaptive intermolecular reactive bond order (AIREBO) potential in the atomistic model, which is carefully weighted by the atomic energy scaling function in the bridging zone. In the continuum model, a thermodynamically rigorous high-order continuum description, considering the symmetries of graphene, is used which is parameterized using full molecular dynamics (MD) simulations. To accurately capture the bending behavior of graphene, a recently developed explicit finite-deformation solid-shell element is used to discretize the continuum domain, and its formulation is modified to include the continuum energy scaling function. To achieve realistic constant-temperature condition (canonical ensemble), the Nosé-Hoover thermostat is used in the full MD domain and also as local thermostats in the bridging domain. 5-value Gear predictor-corrector time integrator is implemented, which is well-suited to be used with the Nosé-Hoover thermostat. Accordingly, the TBDM formulation is modified to work with this time integrator. Some modifications are also made in the TBDM formulation to increase the robustness of the multiscale simulations. Finally, the effectiveness of the proposed multiscale method for graphene is demonstrated by running in-plane shear, out-of-plane bending, and nanoindentation simulations and comparing the results with those obtained from full MD and full finite-element simulations.