Quasicontinuum analysis of defects in solids

E. B. Tadmor, M. Ortiz, R. Phillips

Research output: Contribution to journalArticle

1204 Scopus citations

Abstract

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 A1 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.

Original languageEnglish (US)
Pages (from-to)1529-1563
Number of pages35
JournalPhilosophical Magazine A: Physics of Condensed Matter, Structure, Defects and Mechanical Properties
Volume73
Issue number6
DOIs
StatePublished - Jun 1996

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