In this work a couple stress continuum based elasto-viscoplastic fast Fourier transform model is developed with the intent to study the role of curvatures - gradient of rotation - on the local meso scale and effective macro scale mechanical response of nanocrystalline materials. Development of this model has led to the formulation of an extended periodic Lippmann Schwinger equation that accounts for couple stress equilibrium. In addition to the standard boundary conditions on strain rate and Cauchy stresses, the model allows imposing non-standard couple stress and curvature rate boundary conditions. Application to representative nanocrystalline microstructures reveals that elastic and plastic curvatures accommodate a part of the local and macroscopic Cauchy stresses. Next, grain boundary interfaces are characterized using curvatures that are representative of their structure and defect content. Depending on the magnitude and distribution of these curvatures, local stresses in the grain boundary neighborhood are generated that activate slip systems besides those fulfilling the Schmid criterion. Generation of both polar dislocations and disclinations as a possible plasticity mechanism in nanocrystalline materials is explored. At the macro scale, this results in a strain rate dependent "softening" or the inverse Hall-Petch effect. The modeling framework naturally captures this grain size effect without any ad hoc assumptions.