Localization Analysis of an Energy-Based Fourth-Order Gradient Plasticity Model

Abstract

The purpose of this paper is to provide analytical and numerical solutions of the formation and evolution of the localized plastic zone in a uniaxially loaded bar with variable cross-sectional area. An energy-based variational approach is employed and the governing equations with appropriate physical boundary conditions, jump conditions, and regularity conditions at evolving elasto-plastic interface are derived for a fourth-order explicit gradient plasticity model with linear isotropic softening. Four examples that differ by regularity of the yield stress and stress distributions are presented. Results for the load level, size of the plastic zone, distribution of plastic strain and its spatial derivatives, plastic elongation, and energy balance are constructed and compared to another, previously discussed non-variational gradient formulation.

41 pages, 24 figures; moderate revision after the first round of review, Appendix A re-written completely

References in corpus (1)

• Localization Study of a Regularized Variational Damage Model

Cited by in corpus (6)

• Phase-field modeling of fatigue coupled to cyclic plasticity in an energetic formulation
• A Variational Formulation of Dissipative Quasicontinuum Methods
• Localization Study of a Regularized Variational Damage Model
• A Parameter-Robust Iterative Method for Stokes-Darcy Problems Retaining Local Mass Conservation
• A micromechanics-based variational phase-field model for fracture in geomaterials with brittle-tensile and compressive-ductile behavior
• Stochastic phase-field modeling of brittle fracture: computing multiple crack patterns and their probabilities