A multiscale molecular dynamics method for isothermal dynamic problems using the seamless heterogeneous multiscale method

•We derive the EOM of a multiscale molecular dynamics in a bottom-up approach.•The model is applicable for isothermal dynamical problems and couples FE and MD.•We use the seamless HMM to efficiently couple the coarse and the fine scale.•Dynamical problems (intractable by full MD) are investigated for about a millisecond.

Based on recent developments in Parrinello–Rahman molecular dynamics a hierarchical two-scale molecular dynamics framework is derived that couples a coarse scale local particle dynamics with a fine scale molecular dynamics. This multiscale structure provides a seamless transition from the atomistic to continuum scale for an isothermal problem. The molecular dynamics cells at the fine scale are constrained by the deformation and temperature of the coarse scale grid and supply the coarse scale with the constitutive behaviour of the material computed directly from atomistics. Furthermore, the seamless heterogeneous multiscale method is employed to efficiently perform the time integration by solving the coarse and fine scale equations of motion simultaneously with independent clocks. Numerical examples demonstrate the performance of the proposed multiscale scheme.