Computational Homogenization Method for Atom-to-Continuum Modeling.

Homogenization theory has been well accepted by the applied mechanics modeling community for its ability to integrate small-scale microstructure phenomena into bulk continuum equations using convergent features of asymptotics. This paper describes an extension of the method to handle asymptotically small atomic scale systems at zero temperature embedded within a deforming continuum. A so-called inner displacement naturally arises in the formulation that enables the consideration of distributed anharmonic crystalline effects that would otherwise be unapproachable with bulk continuum methods alone. The result is a simple computational mechanics method that, first, maps instantaneous continuum deformation gradients to deforming defected crystalline arrangements then, second, provides convergent effective material properties to be used for consistent continuum calculations. The intended applications are those involving patterned defects, either in bulk or on surfaces, which allude to possible manufacturing scenarios. Simple 2-D examples are shown for in-plane deformation of graphene possessing various types of point defects. © 2004 American Institute of Physics [ABSTRACT FROM AUTHOR]