Mixed atomistic and continuum methods offer the possibility of carrying out simulations of material properties at both larger length scales and longer times than direct atomistic calculations. The quasicontinuum method links atomistic and continuum models through the device of the finite element method which permits a reduction of the full set of atomistic degrees of freedom. The present paper gives a full description of the quasicontinuum method, with special reference to the ways in which the method may be used to model crystals with more than a single grain. The formulation is validated in terms of a series of calculations on grain boundary structure and energetics. The method is then illustrated in terms of the motion of a stepped twin boundary where a critical stress for the boundary motion is calculated and nanoindentation into a solid containing a subsurface grain boundary to study the interaction of dislocations with grain boundaries.

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Keywords A. Dislocations, A. Grain boundaries, B. Constitutive behaviour, C. Finite elements
Journal Journal of the Mechanics and Physics of Solids
Shenoy, V.B. (V. B.), Miller, R, Tadmor, E.B. (E. B.), Rodney, D. (D.), Phillips, R. (R.), & Ortiz, M. (M.). (1999). An adaptive finite element approach to atomic-scale mechanics - The quasicontinuum method. Journal of the Mechanics and Physics of Solids, 47(3), 611–642.