Study on one-dimensional softening with localization via integrated MPM and SPH

Abstract

Nonlocal elastoplasticity and/or damage models in terms of gradient or integral of strain or internal state variables have been proposed to regularize softening with localization in model-based simulation of failure evolution. For transient problems, the numerical oscillations due to semi-discretization in space make the evaluation of higher order terms a difficult task in avoiding numerical failure such as premature cracking. In this preliminary study, an integrated MPM (material point method) and SPH (smoothed particle hydrodynamics) numerical scheme is proposed to implement a nonlocal model via the gradient of plastic strain, with an application to a one-dimensional bar under impact. The MPM is used to discretize the continuum region without the need for master/slave nodes at the contact surface, while the smoothing operator and particle approximation based on the SPH are adopted on the material points to reduce the unphysical oscillations and facilitate the evaluation of strain gradient. A parametric investigation is performed to illustrate the effects of controlling parameters on the evolution of localized softening. It is demonstrated that integrating nonlocal constitutive modeling with spatial discretization might yield an effective procedure for predicting and evaluating failure evolution.