Interpolation–free discrete modeling with gradient matrix: Case study of edge dislocation in linearly elastic crystal

A meshless and interpolation-free (MIF) method of numerical modeling in solid mechanics has been formulated with a gradient matrix extending the gradient operation to discrete data. Nodal strains and, consequently, stresses in this method are expressed immediately in terms of nodal displacements and the stress divergence in terms of nodal stresses that makes it possible to get the stress balance equation in a truly discrete form. A trial MIF model where nodal points correspond to atom positions is employed for a rectilinear edge dislocation in a linearly elastic crystal. Both the resulting stress level at the dislocation core, close to the theoretical crystal strength, and respective core dimensions prove to be realistic physically whereas calculated long-range stresses asymptotically approach the related continuous fields known in an analytical form for the dislocation in linearly elastic isotropic continuum.