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The gradient operation has been extended to discrete data in terms of nodal
coordinates. On this ground, the nodal strains and related stresses are expressed directly in
terms of nodal displacements and the stress divergence in terms of nodal stresses. To make
use of truly discrete modeling in computational solid mechanics, the stress balance equation is
formulated. For a case study, the latter is applied to an edge dislocation where atom positions
of a dislocated crystal are taken for nodal points. Both the resulting stress level at the
dislocation core close to the theoretical strength and the corresponding core dimensions prove
to be realistic physically, whereas the long-range nodal stresses asymptotically approach the
virtual continuous fields known in an analytical form.
Keywords: discrete gradient, edge dislocation, element-free model, shape function, stress balance |
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