Analysis of Tikhonov Regularization on the Integral-Type Nonlocal Plasticity Model

Abstract

Tikhonov regularization on the integral-type nonlocal plasticity model is proposed to obtain a mesh-independent solution of strain localization. A detailed parametric study on the Tikhonov-regularized model is carried out for a one-dimensional and a two-dimensional problem. The influence of the regularization parameter, the tolerance of the nonlocal yield criterion, and the internal length scale on the finite-element solutions are examined. The width of the localization zone was found to be six times the internal length scale for a Gaussian-type weighting function. The solutions of the two-dimensional shear banding problem are compared with those of the one-dimensional strain localization. With the proposed model, no additional boundary conditions have to be introduced in the constitutive level, and only C0 continuity is needed at element interfaces.