QUASI-CONTINUUM ANALYSIS OF DEFECTS IN SOLIDS

We develop a method which permits the analysis of problems requiring t he simultaneous resolution of continuum and atomistic length scales-an d associated deformation processes-in a unified manner. A finite eleme nt methodology furnishes a continuum statement of the problem of inter est and provides the requisite multiple-scale analysis capability by a daptively refining the mesh near lattice defects and other highly ener getic regions. The method differs from conventional finite element ana lyses in that interatomic interactions are incorporated into the model through a crystal calculation based on the local state of deformation . This procedure endows the model with crucial properties, such as sli p invariance, which enable the emergence of dislocations and other lat tice defects. We assess the accuracy of the theory in the atomistic li mit by way of three examples: a stacking fault on the (111) plane, and edge dislocations residing on (111) and (100) planes of an aluminium single crystal. The method correctly predicts the splitting of the (11 1) edge dislocation into Shockley partials. The computed separation of these partials is consistent with results obtained by direct atomisti c simulations. The method predicts no splitting of the Al Lomer disloc ation, in keeping with observation and the results of direct atomistic simulation. In both cases, the core structures are found to be in goo d agreement with direct lattice statics calculations, which attests to the accuracy of the method at the atomistic scale.