This paper presents constitutive models for the finite-strain, macroscopic response of porous viscoplastic single crystals and polycrystals. The model accounts explicitly for the evolution of the average lattice orientations, as well as the porosity, average shape and orientation of the voids, by means of appropriately defined microstructural variables playing the role of internal variables and serving to characterize the evolution of both the “crystallographic” and “morphological” anisotropy of the porous single crystals. The model makes use of the fully optimized second-order variational method , together with the iterated homogenization approach , to determine the instantaneous effective response of the porous single crystals with fixed values of the microstructural variables. Consistent homogenization estimates for the average strain rate and vorticity fields in the phases are then used to derive evolution equations for the associated microstructural variables. The model is predictive, requiring no fitting parameters, and applies for porous viscoplastic single crystals and polycrystals with general crystal anisotropy, average void shape and orientation, and loading conditions. Results for both the instantaneous response and the evolution of the microstructure will be presented for porous FCC and HCP single crystals and polycrystals under a wide range of loading conditions, and good agreement with available FEM results  will be shown.
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