Combined stretching and twisting of a circular thin-walled tube of second gradient plastic material

The objective of this work is to derive an analytical solution for the problem of a second gradient plastic circular thin-walled tube in combined tension and torsion loading conditions. Explicit expressions for the ordinary and higher-order stresses, strain rate and its gradient, and displacement are obtained. For comparison purpose, we also present the analytical solution for the same problem when the thin-walled tube is made of classical (von Mises) plastic metals. The newly micromorphic model based solution reduces to that of the (ordinary) von Mises one when the characteristic length scale approaches zero.