Simple tension three ways

Abstract

The consequences of using a principal Cauchy stress formulation of simple tension of cuboid specimens are explored within the context of incompressible isotropic materials, with the prototypical neo-Hookean material used to illustrate the main ideas. When simple tension is defined in this way it is shown that there are three natural Cartesian forms for the Cauchy stress: the conventional form, a plane stress form and a uniform stress form. A deformation consistent with each of these forms is obtained for the neo-Hookean material and it is shown that there are some counter-intuitive effects. It is also shown that the plane stress form of simple tension could alternatively describe the effect of applying equal and opposite forces to diagonally opposite edges of a cuboid specimen, with the uniform stress form describing the effect of applying these forces to diagonally opposite corners of a cuboid.