  We show that simple shear and pure shear form two groups of transformations
with different properties. The equivalent strain is viewed as an external
control parameter of the deformation process at low homologous temperatures.
The von Mises strain satisfies group-theoretic properties of both groups,
supporting its use for measuring the equivalent strain. The Hencky strain, on
the other hand, does not satisfy the simple shear group properties, implying
that it is not appropriate for measuring the equivalent strain in simple shear.
The paper also proposes a hypothesis explaining the absence of metal hardening
in large simple shear deformations. This hypothesis explains why excluding
rotations as prescribed by the finite strain theory is not valid.
