An adaptive finite element approach to atomic-scale mechanics - The quasicontinuum method

V. B. Shenoy; R. Miller; E. B. Tadmor; D. Rodney; R. Phillips; M. Ortiz

doi:10.1016/S0022-5096(98)00051-9

An adaptive finite element approach to atomic-scale mechanics - The quasicontinuum method

V. B. Shenoy, R. Miller, E. B. Tadmor, D. Rodney, R. Phillips, M. Ortiz

Aerospace Engineering and Mechanics

Research output: Contribution to journal › Article › peer-review

532 Scopus citations

Abstract

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.

Original language	English (US)
Pages (from-to)	611-642
Number of pages	32
Journal	Journal of the Mechanics and Physics of Solids
Volume	47
Issue number	3
DOIs	https://doi.org/10.1016/S0022-5096(98)00051-9
State	Published - Mar 1 1999

Bibliographical note

Funding Information:
We thank C. Briant, R. Clifton, B. Gerberich, P. Hazzledine, S. Kumar and A. Schwartzman for many stimulating discussions, S. W. Sloan for use of his Delaunay triangulation code and M. Daw and S. Foiles for use of their Dynamo code. This work was supported by the AFOSR through grant F49620-95-I-0264, the NSF through grants CMS-9414648 and DMR-9632524, and the DOE through grant DE-FG02-95ER14561. R.M. acknowledges support of the NSERC.

Keywords

A. Dislocations
A. Grain boundaries
B. Constitutive behaviour
C. Finite elements

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10.1016/S0022-5096(98)00051-9

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abstract = "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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note = "Funding Information: We thank C. Briant, R. Clifton, B. Gerberich, P. Hazzledine, S. Kumar and A. Schwartzman for many stimulating discussions, S. W. Sloan for use of his Delaunay triangulation code and M. Daw and S. Foiles for use of their Dynamo code. This work was supported by the AFOSR through grant F49620-95-I-0264, the NSF through grants CMS-9414648 and DMR-9632524, and the DOE through grant DE-FG02-95ER14561. R.M. acknowledges support of the NSERC.",

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AU - Phillips, R.

AU - Ortiz, M.

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N2 - 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.

AB - 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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An adaptive finite element approach to atomic-scale mechanics - The quasicontinuum method

Abstract

Bibliographical note

Keywords

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