quasicontinuum

Quasicontinuum (QC) is a multiscale computational method for crystalline solids that couples atomistic models with continuum mechanics to simulate materials at reduced cost. It replaces full atomistic detail with a continuum description away from defects while retaining atomistic resolution in regions where atomic-scale phenomena are important. The method relies on representing the crystal by a coarse lattice of representative atoms and using interpolation to reconstruct the positions of all atoms. The total energy is assembled from two parts: an atomistic energy computed with interatomic potentials in the highly resolved region, and a continuum (elastic) energy derived from the Cauchy–Born rule in the far field. The two descriptions are stitched together, often with a bridging region, producing an energy-based formulation that yields equilibrium by energy minimization.

The practical gain of QC is a dramatic reduction in degrees of freedom compared with full atomistic simulations, while preserving essential defect physics such as dislocations, cracks, and interfaces. Variants include energy-based QC and force-based QC (QCF) to address coupling issues, and adaptive QC approaches that refine the representation near defects or evolving features. The method is commonly implemented with a mesh of representative atoms and interpolation schemes to reconstruct atomic positions, along with a repository of interatomic potentials for the atomistic zones.

Limitations include dependence on the validity of the Cauchy–Born approximation, especially near complex defect cores where nonlocal effects are important. Challenges remain for highly nonlinear, finite-temperature, or dynamic problems, and ghost forces can arise in some coupling schemes. QC was developed in the late 1990s by Tadmor, Ortiz, and Phillips and has since become a widely used tool in materials science for multiscale modeling of crystalline systems.