A method was developed which permitted the analysis of problems that required the simultaneous resolution of continuum and atomistic length scales, and associated deformation processes, in a unified manner. Finite element methods yielded a continuum statement of the problem, and provided the possibility of multiple-scale analysis by refining the mesh near to lattice defects and other highly energetic regions. The method differed from conventional finite element analyses in that interatomic interactions were incorporated into the model via a crystal calculation that was based upon the local deformation state. This imparted essential properties, such as slip invariance, to the model. This permitted the emergence of dislocations and other lattice defects. The accuracy of the theory in the atomistic limit was assessed by using 3 examples. These were a stacking fault on the (111) plane, and edge dislocations on the (111) and (100) planes, of an Al monocrystal. It was found that the method correctly predicted the splitting of the (111) edge dislocation into Shockley partials. The predicted separation of these partial dislocations was consistent with the results which were predicted by direct atomistic simulations. The method did not predict any splitting of the Al Lomer dislocation. This conclusion was in accord with observations and with the results of direct atomistic simulations. In both cases, the core structures were found to be in good agreement with direct lattice statics calculations.

Quasi-Continuum Analysis of Defects in Solids. E.B.Tadmor, M.Ortiz, R.Phillips: Philosophical Magazine A, 1996, 73[6], 1529-63