Micromechanics-based modeling of plastic polycrystals: an affine formulation

Recent comparisons of predictions associated with Hill’s original ‘incremental’ formulation for the self-consistent modelling of elastoplastic polycrystals with a newly available nonlinear upper bound for the moduli have brought to light the fact that this formulation leads to a frequent violation of this bound. This conclusion has motivated the conception of a new formulation, called the ‘affine formulation’, which is expected to yield softer predictions. The principle of this formulation is first reported for the simpler case of nonlinear elasticity (or viscosity) and compared with other approaches. It is then extended to cases for which the current responses depend on the loading path, with specification to the self-consistent scheme in order to model transient responses of polycrystals; though no variational approach exists in these cases, the obtained predictions can be considered as improved ones since they are shown to be, as expected, softer than those derived from other models.