A nonlocal plasticity formulation for the material point method

0045-7825/$ see front matter 2012 Elsevier B.V. A http://dx.doi.org/10.1016/j.cma.2012.03.007 ⇑ Corresponding author. E-mail addresses: [email protected], jeff788@g 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. 2012 Elsevier B.V. All rights reserved.