Concurrent coupling of atomistic and continuum models at finite temperature

A concurrent multiscale method for coupling discrete (atomistic) and continuum models at finite temperatures is presented. Motion of atoms is governed by an inter-atomic potential and is represented by molecular dynamics. A thermo-mechanical continuum defined by standard differential equations of conservation of momentum and heat transport is used. The coupling is performed by an interface region where the two models overlap. The phonon spectrum of the discrete region is divided into a low frequency part which is transferred to the continuum model as mechanical waves, and a high frequency component which is modeled in the continuum as diffusive heat transport. Seamless mechanical coupling is ensured by imposing weak compatibility of displacements in the interface region. The method is implemented in 1D and full bi-directional thermal and mechanical coupling is demonstrated in thermodynamic equilibrium and in non-equilibrium.