On boundary conditions and plastic strain-gradient discontinuity in lower-order gradient plasticity

Through linearized analysis and computation, we show that lower-order gradient plasticity is compatible with boundary conditions, thus expanding its predictive capability. A physically motivated gradient modification of the conventional Voce hardening law is shown to lead to a convective stabilizing effect in 1-D, rate-independent plasticity. The partial differential equation is genuinely nonlinear and does not arise as a conservation law, thus making the task of inferring plausible boundary conditions a delicate matter. Implications of wave-type behavior in rate-independent plastic response (under conditions of static equilibrium) are analyzed with a discussion of an appropriate numerical algorithm. Example problems are solved numerically, showing the robustness and simplicity of physically motivated lower-order gradient plasticity. The 3-D case and rate-dependent constitutive assumptions are also discussed.