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We show that simple shear and pure shear form two groups of transformationswith different properties. The equivalent strain is viewed as an externalcontrol 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, onthe other hand, does not satisfy the simple shear group properties, implyingthat it is not appropriate for measuring the equivalent strain in simple shear.The paper also proposes a hypothesis explaining the absence of metal hardeningin large simple shear deformations. This hypothesis explains why excludingrotations as prescribed by the finite strain theory is not valid.

Equivalent Strain in Simple Shear Deformations