Localization Analysis of an Energy-Based Fourth-Order Gradient Plasticity Model
For researchers in computational mechanics, this provides a variational framework for gradient plasticity, but the work is incremental, extending existing models to specific examples.
This paper derives analytical and numerical solutions for localized plastic zone formation in a uniaxially loaded bar using an energy-based fourth-order gradient plasticity model, comparing results with a non-variational formulation. Key outcomes include load level, plastic zone size, and energy balance.
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.