In the framework of a model of a micropolar medium (Cosserat continuum), which is a medium with couple stress and rotational interaction of particles, finite deformations families are found. For these families, the sysTem of equilibrium equations is reduced to the system of nonlinear ordinary differential equations. First integrals of the equations are constructed. The problems of bending and torsion of prismatic elastic bodies with continuously distributed dislocations under large deformations are considered. A number of exact solutions of micropolar bodies with large deformations and bodies with distributed dislocations is represented.
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