A nonlocal lattice particle model for J2 plasticity

In virtue of their intrinsic integro-differential formulation of underlying physical behavior of materials, discontinuous computational methods are more beneficial over continuum-mechanics-based approaches for materials failure modeling and simulation. However, application of most discontinuous methods is limited to elastic/brittle materials, which is partially due to their formulations are based on force and displacement rather than stress and strain measures as are the cases for continuous approaches. In this article, we formulate a nonlocal maximum distortion energy criterion in the framework of a lattice particle model for modeling of elastoplastic materials. Similar to the maximum distortion energy criterion in continuum mechanics, the basic idea is to decompose the energy of a discrete material point into dilatational and distortional components, and plastic yielding of bonds associated with this material point is assumed to occur only when the distortional component reaches a critical value. However, the formulated yield criterion is nonlocal since the energy of a material point depends on the deformation of all the bonds associated with this material point. Formulation of equivalent strain hardening rules for the nonlocal yield model was also developed. Compared to theoretical and numerical solutions of several benchmark problems, the proposed formulation can accurately predict both the stress-strain curves and the deformation fields under monotonic loading and cyclic loading with different strain hardening cases.