Multiresolution molecular mechanics: Statics

This paper presents a new concurrent atomistic-continuum coupling method called the multiresolution molecular statics (MMS). By introducing a novel energy sampling framework, MMS aims at accurately and efficiently approximating the atomic energy of the system at different resolutions without the cumbersome interfacial treatment in existing methods. The key features of the MMS method are: (1) consistency with the atomistics framework, (2) consistency with the order of shape functions introduced, and (3) flexibility in energy approximation with respect to accuracy and efficiency. Under the energy sampling framework, several sampling schemes have been devised and tested for interface compatibility, and compared to existing methods. Sources of errors in the different approximations have been identified. The proposed MMS method demonstrates very good accuracy in solving crack propagation and surface relaxation problems when compared to full molecular statics.