In this paper a method is presented for torsional analysis of non-homogeneous tubes with arbitrarily shaped cross-sections. A previously presented method based on Bredt’s theory is extended to achieve formulas for torsional analysis. Shear modulus varies through the thickness according to a power law distribution. To validate the accuracy of the presented formulas for angle of twist and shear s...

In the present work we follow the breakdown of pairs of counter-rotating vortices (CVP) and the consequence formation of packets of hairpins in uniform shear flows. We employ a recent developed method which is capable of following (numerically) the evolution of finite-amplitude localized vortical disturbances embedded in shear flows. The solution is carried out using Lagrangian variables in Fou...

We present some experimental and numerical results based on a simple model designed to give an estimate for the width of a shear zone. We conclude that the observed finite size of the shear zone can be associated with the propagation of the force lines inside the medium. The model, based on a simple argument on the force distribution and dilatancy, predicts a width of about ten grain diameters.