Quasicontinuum analysis of defects in solids
We develop a method which permits the analysis of problems requiring the simultaneous resolution of continuum and atomistic length scales-and associated deformation processes-in a unified manner. A finite element methodology furnishes a continuum statement of the problem of interest and provides the requisite multiple-scale analysis capability by adaptively refining the mesh near lattice defects and other highly energetic regions. The method differs from conventional finite element analyses 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 slip invariance, which enable the emergence of dislocations and other lattice defects. We assess the accuracy of the theory in the atomistic limit 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 (111) edge dislocation into Shockley partials. The computed separation of these partials is consistent with results obtained by direct atomistic simulations. The method predicts no splitting of the Al Lomer dislocation, in keeping with observation and the results of direct atomistic simulation. In both cases, the core structures are found to be in good agreement with direct lattice statics calculations, which attests to the accuracy of the method at the atomistic scale.
© 1996 Taylor & Francis. [Received 10 July 1995 and accepted in revised form 14 October 1995] The authors gratefully acknowledge support from the AFOSR through grant F49620-92-J-0129. R. P. gratefully acknowledges support from NSF under grant number CMS-9414648. This material is also based upon work supported by the National Science Foundation under the Materials Research Group grant no. DMR-9223683. We appreciate comments by R. Clifton, J. Weiner, R. Miller and V. Shenoy.