Two new formulations of micropolar single crystal plasticity were presented within a geometrically linear setting. The construction of yield criteria and flow rules for generalized continuum theories with higher-order stresses could be done in one of two ways: (i) a single criterion could be introduced in terms of a combined equivalent stress and inelastic rate or (ii) or individual criteria could be specified for each conjugate stress/inelastic kinematic rate pair, a so-called multi-criterion theory. Both single and multi-criterion theories were developed and discussed within the context of dislocation-based constitutive models. Parallels and distinctions were made between the proposed theories and some of the alternative generalized crystal plasticity models that could be found in the literature. Parametric numerical simulations of a constrained thin film subjected to simple shear were conducted via finite element analysis using a simplified two-dimensional version of the fully three-dimensional theory to highlight the influence of specific model components on the resulting deformation under both loading and unloading conditions. The deformation behaviour was quantified in terms of the average stress–strain response and the local shear strain and geometrically necessary dislocation density distributions. It was demonstrated that micropolar single crystal plasticity could qualitatively capture the same range of behaviours as slip gradient-based models, while offering a simpler numerical implementation and without introducing plastic slip rates as generalized traction-conjugate velocities subject to an additional microforce balance.

Dislocation-Based Micropolar Single Crystal Plasticity: Comparison of Multi- and Single Criterion Theories. J.R.Mayeur, D.L.McDowell, D.J.Bammann: Journal of the Mechanics and Physics of Solids, 2011, 59[2], 398-422