A nonlocal plasticity formulation for the material point method

摘要

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.