A nonlocal plasticity formulation for the material point method

A new multi-variate fixed-point iteration scheme is devised for solving the coupled dynamic integral equations governing nonlocal plasticity using the material point method (MPM). Novel use of the MPM grid for particle–particle communications results in a simple and efficient, matrix-free method. Moreover, a straightforward method for deriving a convergence criterion for this method is developed and applied to two classical verification problems that are well known to be mesh dependent with a local model, but are shown to be mesh-independent with the new nonlocal MPM formulation.