Guidelines for Constructing Strain Gradient Plasticity Theories

Issues related to the construction of continuum theories of strain gradient plasticity which have emerged in recent years are reviewed and brought to bear on the formulation of the most basic theories. Elastic loading gaps which can arise at initial yield or under imposition of non-proportional incremental boundary conditions are documented and analytical methods for dealing with them are illustrated. The distinction between unrecoverable (dissipative) and recoverable (energetic) stress quantities is highlighted with respect to elastic loading gaps, and guidelines for eliminating the gaps are presented. An attractive gap-free formulation that generalizes the classical 2 J flow theory is identified and illustrated.