Small Deformation Plane Strain Pure Bending of a Sector of a Circular Tube of an Incompressible 3D Cosserat Material

Abstract

Recently, an Eulerian formulation of a nonlinear thermomechanical Cosserat theory of a 3D continuum enriched with a deformable triad of director vectors was developed for anisotropic elastic-inelastic response. To study the influence of the directors on size-dependent response the small deformation purely mechanical equations for this Cosserat continuum are used to formulate and solve the problem of plane-strain pure bending of a circular tube of an elastically isotropic incompressible Cosserat material. Examples present the influences of the stiffness to deformations of the directors and the intrinsic length in the formulation.