Rotation Problems in Simple Shear Deformation

Abstract

According to Cauchy’s theorem of moment equilibrium for all the arbitrary elements of deforming solid materials under loading, a balanced pair of shear stresses orthogonally crossing each other must always be present and is called pure shear stress. This assumption results in a very strange way of explanation that simple shear strain consists of pure shear strain and accompanying rotation because simple shear strain must be identical with pure shear strain. In a series of investigations into the dilemmas of the traditional assumption of shear stress and strain for equilibrium, this paper tries to make clear what is wrong in the treatment of the rotation of a deforming element. The limitation of present tensor analysis is also discussed.