Theory of large-strain torsion of prismatic bodies with moment stresses

The problem of the torsion and tension-compression of a prismatic bar with a stress-free lateral surface is studied using three-dimensional elasticity theory for materials with moment stresses. A substitution is found that allows one to separate one variable in the nonlinear equilibrium equations for a Cosserat continuum and boundary conditions on the lateral surface. This substitution reduces the original spatial problem of the equilibrium of a micropolar body to a two-dimensional nonlinear boundary-value problem for a plane region shaped like the cross section of the prismatic bar. Variational formulations of the two-dimensional problem for the section are given that differ in the sets of varied functions and the constraints imposed on their boundary values.