An analysis of the quasicontinuum method. (English) Zbl 1002.74008

Knap, J.; Ortiz, M.

J. Mech. Phys. Solids 49, No. 9, 1899-1923 (2001).

From the summary: We examine a version of quasicontinuum theory and analyze its accuracy and convergence characteristics. Specifically, we assess the effect of summation rules on accuracy; we determine the rate of convergence of the method in the presence of strong singularities, such as point loads; and we assess the effect of refinement tolerance, which controls the rate at which new nodes are inserted in the model, on the development of dislocation microstructures.

MSC:

74A60	Micromechanical theories
82B21	Continuum models (systems of particles, etc.) arising in equilibrium statistical mechanics

Keywords:

error analysis; nanoindentation; atomistic model; quasicontinuum theory; summation rules; rate of convergence; strong singularities; point loads; dislocation microstructures

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