Multi-scale homogenization procedure for continuum–atomistic, thermo-mechanical problems

A multi-scale algorithm is developed for solving, continuum–atomistic thermo-mechanical problems. The coupling of the two scales occurs through a homogenization procedure. A uniform weighted residual approximation method is used to consistently model the interaction of the continuum and atomistic scales. Implementation of the coupling occurs through the transfer of macroscopic and microscopic variables at the macroscopic gauss points. The mechanism for transfer of atomistic information to the macro-level occurs through the Virial stress and the heat flux vector. A dynamic relaxation procedure is introduced to efficiently compute the coupled equilibrium solutions at the macroscopic and microscopic scales. The algorithm has been successfully tested for thermal stress analysis cases, involving constrained and unconstrained macro-components and fixed temperature distributions. Problems involving varying temperatures and heat transfer have been solved and are shown to be in good agreement with molecular dynamics results.