Element-free numerical modeling with discrete gradient and its application to crystal defects

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.