Modeling and Analysis for Atomistic/Continuum Coupling

Summary:

Atomistic/continuum coupling is playing an increasingly important role in the simulations of material sciences. Among all the methods, the quasicontinuum method is the most successful one in the study of static problems. The accuracy of the quasicontinuum method is studied by reformulating the summation rules in terms of reconstruction schemes for the local atomic environment of the representative atoms. The necessary and sufficient condition for uniform first-order accuracy and, consequently, the elimination of the "ghost force" is formulated in terms of the reconstruction schemes. The quasi-nonlocal approach is examined as a special case of this condition. Examples of reconstruction schemes that satisfy this condition are studied in this work. Transition between atom-based and element-based summation rules are also studied. It is also demonstrated that the existence of the ghost force may lead to large errors.