Elastic-Gap Free Formulation in Strain Gradient Plasticity Theory

Abstract

This article presents an elastic-gap free isotropic higher-order strain gradient plasticity theory that effectively captures dissipation associated to plastic strain gradients. Unlike conventional methods that divide the higher-order stress, this theory focuses on dividing the plastic strain gradient into energetic and dissipative components. The moment stress that arises from minimizing a dissipating potential demonstrates a nonlinear evolution over time, resembling the Armstrong–Frederick nonlinear kinematic hardening rule in classical plasticity. The thermodynamically consistent framework establishes additional dissipation in the dissipation inequality. The energetic moment stress saturates as the effective plastic strain increases during plastic flow. In contrast to the Gurtin-type nonincremental model, the proposed model smoothly captures the apparent strengthening at saturation without causing a stress jump. A passivated shear layer is analytically assessed to demonstrate that the proposed theory exhibits the same amount of dissipation as the existing Gurtin-type model when they show similar shear responses at saturation. It is also shown that the plastic flow remains continuous under nonproportional loading conditions using an intermediately passivated shear layer problem. Finally, the proposed theory is validated against a recent experiment involving combined bending torsion of an L-shaped beam using a 3D finite element solution. Overall, the proposed model provides an alternative approach to evaluating the size effect within the nonincremental isotropic strain gradient plasticity theory without introducing any stress jump.