Solution for the general integral-type nonlocal plasticity model with Tikhonov regularization

A new solution approach, based on Tikhonov regularization on the Fredholm integral equations of the first kind, is proposed to find the approximate solutions of the strain softening problems. In this approach, the consistency condition is regularized with the Tikhonov stabilizers along with a regularization parameter, and the internal variable increments are solved from the resulting Euler's equations. It is shown that, as the regularization parameter is increased, the solutions converge to a unique one. A nonlocal yield condition and a nonlocal return mapping algorithm are proposed to carry out the integration of constitutive equations in the time and spatial domains. A global plastic dissipation principle is proposed to relax the classical local plastic dissipation postulate. Numerical examples show that the proposed approach leads to objective, mesh-independent solutions of the softening-induced localization problems. A comparison of the results from the proposed approach with those from the gradient-dependent plasticity model shows that the two models give close solutions.