From micro- to macro-plasticity: The scale invariance approach

An account of recent contributions to the theory of plasticity advanced by the author and his co-workers is provided with emphasis on deformation-induced anisotropy and texture formation. For the description of these effects, the so-called scale invariance approach is adopted which allows information and constitutive relations pertaining to single slip to be cast in the form of macroscopic constitutive equations. Various phenomenological plasticity models are derived this way with the extra dividend of deducing explicit expressions for the phenomenological coefficients. The method is particularly suited for large deformation anisotropic plasticity, as it reveals the inherent coupling between the evolution of back stress and the plastic spin. Extended models of macroscopic plastic behavior accounting for vertex and texture phenomena can also be obtained by slightly generalizing the kinematics and kinetics of the microscopic configuration to include rate, non-Schmid, secondary slip and grain orientation effects.