On lower order strain gradient plasticity theories

By way of numerical examples, this paper explores the nature of solutions to a class of strain gradient plasticity theories that employ conventional stresses, equilibrium equations and boundary conditions. Strain gradients come into play in these modified conventional theories only to alter the tangential moduli governing increments of stress and strain. It is shown that the modification is far from benign from a mathematical standpoint, changing the qualitative character of solutions and leading to a new type of localization that appears to be unphysical.