The quasicontinuum method: Overview, applications and current directions

The Quasicontinuum (QC) Method, originally conceived and developed by Tadmor, Ortiz and Phillips [1] in 1996, has since seen a great deal of development and application by a number of researchers. The idea of the method is a relatively simple one. With the goal of modeling an atomistic system without explicitly treating every atom in the problem, the QC provides a framework whereby degrees of freedom are judiciously eliminated and force/energy calculations are expedited. This is combined with adaptive model refinement to ensure that full atomistic detail is retained in regions of the problem where it is required while continuum assumptions reduce the computational demand elsewhere. This article provides a review of the method, from its original motivations and formulation to recent improvements and developments. A summary of the important mechanics of materials results that have been obtained using the QC approach is presented. Finally, several related modeling techniques from the literature are briefly discussed. As an accompaniment to this paper, a website designed to serve as a clearinghouse for information on the QC method has been established at www.qcmethod.com. The site includes information on QC research, links to researchers, downloadable QC code and documentation.