  A polycrystalline plasticity model, which incorporates the contribution of
deformation twinning, is proposed. For this purpose, each material point is
treated as a composite material consisting of a parent constituent and multiple
twin variants. In the constitutive equations, the twin volume fractions and
their spatial gradients are treated as external state variables to account for
the contribution of twin boundaries to free energy. The set of constitutive
relations is implemented in a spectral solver, which allows solving the
differential equations resulting from equilibrium and compatibility conditions.
The proposed model is then used to investigate the behavior of a AZ31 magnesium
alloy. For the investigated loading conditions, the mechanical behavior is
controlled by the joint contribution of basal slip and tensile twinning. Also,
according to the numerical results, the development of crystallographic
texture, morphological texture and internal stresses is consistent with the
experimental observations of the literature.
