The Quasicontinuum (QC) method is a mixed continuum and atomistic approach for simulating the mechanical response of polycrystalline materials. The method reproduces the results of fully-atomistic techniques at a fraction of the computational cost. Both zero temperature and finite temperature versions of the method have been developed.
The key idea of zero-temperature QC is the 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 that are closerly approximated by a uniformly strained crystal. The model is adaptively updated as the deformation evolves.
The QC method was originally developed by Ellad B. Tadmor as part of his Ph.D. research in the Division of Engineering at Brown University between 1992 and 1996 under the advisement of Michael Ortiz and 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 , and used to study nanoindentation in thin films .
The work was continued by Vijay B. Shenoy who generalized the method and extended it to treat polycrystalline materials . This work was also done at Brown University as part of Shenoy's Ph.D. research under the advisement of 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 .
Ronald E. 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 ,. This work was part of Miller's Ph.D. work on the generalization of continuum models to include atomistic features carried out at Brown University under the advisement of Rob Phillips.
An important contribution to the method was made by David Rodney while on visit to Brown University. Rodney's work focused on the so-called "ghost forces" which arise at the interface between the nonlocal atomistic regions and surrounding local continuum . Rodney's solution was to introduce the missing forces as dead loads and to iterate until self-consistency is achieved . Rodney also extended the method to three dimensions and used it along with Rob Phillips to study junction formation and destruction between interacting dislocations .
In recent years the method has continued to be developed and enhanced by several different groups.
- Ellad B. Tadmor (currently at the University of Minnesota), in collaboration with the group of Efthimios Kaxiras at Harvard University, extended the method to treat multilattice crystal materials  and used it to study nanoindentation into silicon single crystals , and polarization switching in ferroelectric materials . More recently, together with Ryan Elliott (University of Minnesota), Tadmor has applied multilattice QC to shape-memory alloys and developed a new tecnhnique called cascading Cauchy-Born kinematics to address unit cell extension during phase transformations .
- Michael Ortiz (Caltech) and Jarek Knap (currently at ARL) have introduced a fully-nonlocal three-dimensional version of the method (we refer to as "cluster QC")  and used it study nanoindentation. This version of the method has continued to be extended in a variety of ways since its introduction. More information on Cluster QC is available on the Ortiz group website, and is not discussed further on this website.
- Ellad B. Tadmor, Gang Lu (currently at California State University, Northridge) and Efthimios Kaxiras (Harvard) developed a QC method which includes a density functional theory (DFT) region within the empirical atomistic region (referred to as "QCDFT") .
- Ronald E. Miller (Carleton University) in collaboration with William A. Curtin (Brown University) developed a technique called coupled atomistic discrete dislocation (CADD) for extracting dislocations from the nonlocal region and representing them by their elastic fields in the local region . Without the dislocation aspect of CADD, it corresponds to a force-based QC method.
- Laurent M. Dupuy (currently at CEA/Saclay) together with Ellad B. Tadmor (U. Minnesota), Ronald E. Miller (Carleton) and Rob Phillips (Caltech) developed a finite temperature version of the QC method, so-called "hot-QC" . This approach is based on earlier work by Vijay B. Shenoy (Indian Institute of Science) . At finite temperature, the method makes use of the local harmonic approximation to estimate the entropy of the atoms not explicitly represented in the model. A subtle effect, whose correct treatment is necessary for accurate results, is the so-called mesh entropy. This treatment is described in chapter 13 of the book by Tadmor and Miller.
- Numerical analysis of the QC method has been carried out by several groups including those of Claude Le Bris (ENPC, France), Weinan E (Princeton University), Mitchell Luskin (University of Minnesota), and Christoph Ortner (University of Warwick). See the publication list for works by these authors.
A list of resources discussing the theory and implementation of the QC method is given here.The QC website is a joint project of Ellad Tadmor and Ronald Miller. For more information, visit the contact page.