Localization analysis of variationally based gradient plasticity model

TL;DR

This paper develops analytical solutions for localized plastic zones in a variable cross-section bar using gradient plasticity with softening, linking load, plastic zone size, and strain distribution.

Contribution

It introduces a variational gradient plasticity formulation with explicit solutions for localization, expanding understanding of softening and plastic zone evolution.

Findings

Derived relations between load, plastic zone size, and strain distribution.

Compared new gradient formulation with previous models.

Provided analytical solutions for different stress distribution cases.

Abstract

The paper presents analytical or semi-analytical solutions for the formation and evolution of localized plastic zone in a uniaxially loaded bar with variable cross-sectional area. A variationally based formulation of explicit gradient plasticity with linear softening is used, and the ensuing jump conditions and boundary conditions are discussed. Three cases with different regularity of the stress distribution are considered, and the problem is converted to a dimensionless form. Relations linking the load level, size of the plastic zone, distribution of plastic strain and plastic elongation of the bar are derived and compared to another, previously analyzed gradient formulation.