A three-layer-mesh bridging domain for coupled atomistic–continuum simulations at finite temperature: Formulation and testing

Although concurrent multiscale methods have been well developed for zero-temperature simulations, improvements are needed to meet challenges pertaining to finite-temperature simulations. Bridging domain method (BDM) is one of the most efficient and widely-used multiscale atomistic–continuum techniques. It is recently revealed that the BDM coupling algorithm has a cooling effect on the atoms in the bridging domain (BD), and application of thermostats to rectify the cooling effect in the original BDM formulation is unstable. We propose improvement of the BDM formulation for finite-temperature simulations by employing a three-layer mesh structure in the BD, consisting of coarse, meso, and atomic meshes. The proposed method uses a mesh-independent physics-based discrimination between thermal and mechanical waves to define and introduce a meso mesh that is independent of the finite-element (FE) mesh. Temperature stability in the BD is achieved by constraining only the mechanical part of atomic motion to the FE displacements while unconstrained thermal vibrations are thermostatted using local thermostats in the BD. The new architecture of three-layer-mesh BD effectively mitigates the temperature cooling effect encountered by the conventional BDM as well as suppresses the spurious mechanical wave reflection. Numerical simulations have shown the robustness and accuracy of the proposed multiscale method at finite temperature.