Generalized mathematical homogenization of atomistic media at finite temperatures in three dimensions

We derive thermo-mechanical continuum equations from Molecular Dynamics (MD) equations using the Generalized Mathematical Homogenization (GMH) theory developed by the authors for 0 K applications. GMH constructs an array of atomistic unit cell problems coupled with a thermo-mechanical continuum problem. The unit cell problem derived is a molecular dynamics problem defined for the perturbation from the average atomistic displacements subjected to the deformation gradient and temperature extracted from the continuum problem. The coarse scale problem derived is a constitutive law-free continuum thermo-mechanical equation. Attention is restricted to heat transfer by lattice vibration (phonons). The method is verified on several model problems against the reference molecular dynamics solution. (c) 2006 Elsevier B.V. All rights reserved.