The Quasicontinuum Method: Theory and Applications
The quasicontinuum (QC) method has become a popular technique to bridge the gap between atomistic and continuum length scales in crystalline solids. In contrast to many other concurrent scale-coupling methods, the QC method only relies upon constitutive information on the lowest scale (viz., on interatomic potentials) and thus avoids empirical constitutive laws at the larger scales. This is achieved by the application of a seamless coarse-graining scheme to the discrete atomistic ensemble and the careful selection of a small set of representative atoms. Since its inception almost two decades ago, many different variants and flavors of the QC method have been developed, not only to study the mechanics of solids but also to describe such physical phenomena as mass and heat transfer, or to efficiently describe fiber networks and truss structures. Here, we review the theoretical fundamentals and give a (non-exhaustive) overview of the state of the art in QC theory, computational methods, and applications. We particularly emphasize the fully nonlocal QC formulation which adaptively ties atomistic resolution to moving defects, and we illustrate simulation results based on this framework. Finally, we point out challenges and open questions associated with the QC methodology.