A unifying treatise of variational principles for two types of micropolar continua

The objective of this work is to elaborate upon the variational setting for micropolar continua with constrained and unconstrained rotations. To this end, several mixed variational principles and their regularizations are considered for both the geometrically linear and nonlinear case. The interrelation between the different formulations are highlighted. The most advantageous result is obtained by translating the insight gained for the geometrically linear case to the geometrically nonlinear case involving large strains and large rotations. It turns out that a particular micropolar description involves standard constitutive models for the symmetric stress part together with a nonsymmetric penalty stress thus circumventing to describe the constitutive law in terms of a nonsymmetric strain measure.