Generalized Mathematical Homogenization: From theory to practice

A Generalized Mathematical Homogenization (GMH) theory for coupling atomistic and continuum descriptions at finite temperature has been extended to account for many-body potentials. GMH gives rise to the constitutive law-free coarse scale equations where coupled continuum thermo-mechanical equations are directly derived from molecular dynamics equations. An integrated computational approach, which seamlessly integrates ABAQUS for coarse scale (finite element method) computations with a molecular dynamics code, has been developed. The accuracy and efficiency of the method has been studied for crystal silicon structures including failure predictions of nanowires.