Parametric Study on an Integral-Type Nonlocal Elastoplasticity Model Regularized with Tikhonov-Phillips Method

Abstract

An integral-type nonlocal elastoplasticity model is proposed and formulated in a one-dimensional scenario to address the strain-softening problem. This nonlocal model includes not only the nonlocal plasticity but also the nonlocal elasticity. The resulting elastic constitutive equation and the plastic consistency condition are ill-posed Fredholm integral equations of the first kind whose solutions are instable without appropriate regularization. In this paper, the Tikhonov-Phillips regularization method is used to reformulate the integral-differential consistency condition to obtain an approximate solution of the local internal variable, which is stable and smooth. A detailed parametric study is carried out to examine the influences of the regularization parameter, the internal length scale, the plastic modulus ratio, and the tolerance of the nonlocal yield condition on the regularized solutions. A numerical example shows that the solutions from the proposed model and the regularization method are mesh-independent. A comparison of the results from the proposed model with those from the nonlocal plasticity model and from the gradient-dependent plasticity model shows good agreement.