A reformulation of strain gradient plasticity

A class of phenomenological strain gradient plasticity theories is formulated to accommodate more than one material length parameter. The objective is a generalization of the classical J2 3ow theory of plasticity to account for strain gradient e4ects that emerge in deformation phenomena at the micron scale. A special case involves a single length parameter and is of similar form to that proposed by Aifantis and co-workers. Distinct computational advantages are associated with this class of theories that make them attractive for applications requiring the generation of numerical solutions. The higher-order nature of the theories is emphasized, involving both higher-order stresses and additional boundary conditions. Competing members in the class of theories will be examined in light of experimental data on wire torsion, sheet bending, indentation and other micron scale plasticity phenomena. The data strongly suggest that at least two distinct material length parameters must be introduced in any phenomenological gradient plasticity theory, one parameter characterizing problems for which stretch gradients are dominant and the other relevant to problems when rotation gradients (or shearing gradients) are controlling. Flow and deformation theory versions of the theory are highlighted that can accommodate multiple lengt