L. E. Shilkrot and W. A. Curtin and R. E. Miller
Journal of the Mechanics and Physics of Solids, 50, 2085–2106 (2002).
A method is introduced for reducing the degrees of freedom in simulations of mechanical behavior of materials without sacrificing important physics. The method essentially combines the quasicontinuum (QC) method with continuum defect models such as the discrete dislocation (DD) method. The QC formulation is used to couple a fully atomistic region to a defect-free elastic continuum. Defects existing in the elastic continuum region of the full problem of interest are treated by the DD-like methods with special boundary conditions. The full coupled problem is then solved by an Eshelby-like procedure involving superposition of the QC and DD problems, and is appropriate in both 2d and 3d. Special attention is given to dealing with dislocation defects. A procedure for the "passing" of dislocation defects from the atomistic to the continuum description in 2d problems is also presented. The overall 2d method with dislocation defects is validated by comparing the predictions of the coupled model to "exact" fully atomistic models for several equilibrium dislocation geometries and a nanoindentation problem in aluminum, and excellent agreement is obtained. The method proposed here should find application to a broad host of problems associated with the multiscale modeling of atomistic, nano- and micromechanical behavior of crystalline solids under mechanical loads.