A time-discontinuous elasto-plasticity formalism to simulate instantaneous plastic flow bursts

TL;DR

This paper introduces a novel continuum mechanics-based model that captures the intermittent, burst-like nature of plastic flow at the micro-scale by incorporating a plastic deformation threshold, enabling more realistic simulations of plasticity phenomena.

Contribution

A new time-discontinuous formalism for elasto-plasticity is proposed, accounting for plastic flow bursts within finite element simulations, bridging the gap between micro-scale intermittence and continuum models.

Findings

Reproduces spatiotemporal intermittence of plastic flow

Captures self-organization of plastic deformation

Integrates threshold-based plasticity into FE simulations

Abstract

Plastic flow is conventionally treated as continuous in finite element (FE) codes, whether in isotropic, anisotropic plasticity, or crystal plasticity. This approach, derived from continuum mechanics, contradicts the intermittent nature of plasticity at the elementary scale. Understanding crystal plasticity at micro-scale opens the door to new engineering applications, such as microscale machining. In this work, a new approach is proposed to account for the intermittence of plastic deformation while remaining within the framework of continuum mechanics. We introduce a material parameter, the plastic deformation threshold, denoted as $\Delta p_{min}$, corresponding to the plastic deformation carried by the minimal plastic deformation burst within the material. The incremental model is based on the traditional predictor-corrector algorithm to calculate the elastoplastic behavior of a material subjected to any external loading. The model is presented within the framework of small deformations for von Mises plasticity. To highlight the main features of the approach, the plastic strain increment is calculated using normality rule and consistency conditions, and is accepted only if it exceeds $\Delta p_{min}$. To achieve this, a time-discontinuous generalization of the Karush-Kuhn-Tucker (KKT) conditions is proposed. The simulations show that the introduction of the plastic threshold allows for the reproduction of the spatiotemporal intermittence of plastic flow, capturing the self-organization of plastic flow in complex loading scenarios within an FE model.