Mixed atomistic and continuum methods offer the possibility of carrying outsimulations of material properties at both larger length scales and longertimes than direct atomistic calculations. The quasi-continuum method linksatomistic and continuum models through the device of the finite element methodwhich permits a reduction of the full set of atomistic degrees of freedom. Thepresent paper gives a full description of the quasicontinuum method, withspecial reference to the ways in which the method may be used to model crystalswith more than a single grain. The formulation is validated in terms of aseries of calculations on grain boundary structure and energetics. The methodis then illustrated in terms of the motion of a stepped twin boundary where acritical stress for the boundary motion is calculated and nanoindentation intoa solid containing a subsurface grain boundary to study the interaction ofdislocations with grain boundaries.
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