  For homogeneous, isotropic, nonlinearly elastic materials, the form of the
homogeneous deformation consistent with the application of a Cauchy shear
stress is derived here for both compressible and incompressible materials. It
is shown that this deformation is not simple shear, in contrast to the
situation in linear elasticity. Instead, it consists of a triaxial stretch
superposed on a classical simple shear deformation, for which the amount of
shear cannot be greater than 1. In other words, the faces of a cubic block
cannot be slanted by an angle greater than 45deg by the application of a pure
shear stress alone. The results are illustrated for those materials for which
the strain energy function does not depend on the principal second invariant of
strain. For the case of a block deformed into a parallelepiped, the tractions
on the inclined faces necessary to maintain the derived deformation are
calculated.
