Torsion of cylindrical bodies with varying strain properties

Abstract

We analyze the results of experimental studies of effective strain properties of damaged, porous, and other inhomogeneous materials and study the main laws of their behavior under strain. We consider the possible versions of constitutive relations taking account of the dependence of the properties of the media under study on the loading conditions or the strain conditions and the relations between the shear and bulk strains. Since the traditional statement of the torsion problems for bodies with such properties cannot be used, we analyze the strain consistency equations and the relations between the strains and displacements in cylindrical coordinates and obtain expressions for the displacements in an appropriate generalized form, which can be used not only for the torsion problems. We study how the distributions of displacements, strains, and stresses under torsion depend on the parameter characterizing the susceptibility of the material strain properties to variations in the stress state type. We show that, in the case of torsion of a cylinder of circular cross-section, there is no deplanation of the cross-section, just as in the classical solution, but the distributions of displacements, strains, and stresses significantly differ from the well-known solutions.