The key idea is that of selective representation of atomic degrees of freedom. Instead of treating all atoms making up the system, a small relevant subset of atoms is selected to represent, by appropriate weighting, the energetics of the system as a whole. Based on their kinematic environment, the energies of individual "representative atoms" are computed either in nonlocal fashion in correspondence with straightforward atomistic methodology or within a local approximation as befitting a continuum model. The representation is of varying density with more atoms sampled in highly deformed regions (such as near defect cores) and correspondingly fewer in the less deformed regions further away, and is adaptively updated as the deformation evolves.

The QC method was originally developed by Dr. Ellad B. Tadmor as part of his Ph.D. research at the department of Mechanics of Solids and Structures at Brown University between 1992 and 1996 under the advisement of Prof. Michael Ortiz and Prof. Rob Phillips. The method was applied to single crystal fcc metals and shown to reproduce Lattice Statics results for a variety of line and surface defects [1],[2] and used to study nanoindentation in thin films [11].

The work was continued by Dr. Vijay B. Shenoy who generalized the method and extended it to treat polycrystalline materials [10]. This work was also done at Brown University as part of Dr. Shenoy's Ph.D. research under the advisement of Prof. Rob Phillips. The generalized method was applied to a number of problems including the interaction of dislocations with grain boundaries and the mechanics of steps on grain boundaries [3].

Dr. Ron Miller extended the method to study fracture mechanics at the atomic scale. The effect of grain orientation on fracture and the interaction of cracks with grain boundaries was investigated [5],[7]. This work was part of Dr. Miller's Ph.D. work on the generalization of continuum models to include atomistic features carried out at Brown University under the advisement of Prof. Rob Phillips.

An important contribution to the method was made by Dr. David Rodney while on visit to Brown University. Dr. Rodney's work focused on the so-called "ghost forces" which arise at the interface between the nonlocal atomistic regions and surrounding local continuum. Dr. Rodney's solution was to introduce the missing forces as dead loads and to iterate until self-consistency is achieved [10]. Dr. Rodney also extended the method to three dimensions and used it along with Prof. Rob Phillips to study junction formation and destruction between interacting dislocations [9].

In recent years the method has continued to be developed and enhanced by several different groups. Dr. Tadmor, currently at the Department of Mechanical Engineering at the Technion in Israel, in collaboration with the group of Prof. Efthimios Kaxiras at Harvard University, extended the method to treat complex Bravais lattice materials [8] and used it to study nanoindentation into silicon single crystals [14],[21] and polarization switching in ferroelectric materials. Prof. Ortiz, currently at the Graduate Aeronautical Labsat Caltech, and Dr. Jarek Knap have introduced a fully nonlocal three-dimensional version of the method [20] and used it study nanoindentation. Prof. Ortiz is also collaborating with Prof. Emily Carter at UCLA on incorporating ab initio methods into the method instead of empirical potentials. Dr. Miller, currently at the Department of Mechanical and Aerospace Engineering at Carleton University in Canada in collaboration with Prof. Bill Curtin at Brown University are working on a technique for extracting dislocations from the nonlocal region and representing them by their elastic fields in the local region.

A recent review of the quasicontinuum method discussing its theory and applications has been completed by Ron Miller and Ellad Tadmor. The review will appear in the Journal of Computer-Aided Materials Design. A preprint of the review (5.4 Mb) may be downloaded here.

This website serves as a clearinghouse for QC-related information. It includes a list of publications on the QC method and applications of the QC method; a list of people involved in QC research; a list of links of interest to QC researchers; and download of QC method software, documentation and test cases. The software is is made freely available, subject to the copyright terms specified, in order to promote QC research.