Equivalent strain in simple shear deformation described by using the Hencky strain

The Hencky strain is an appropriate measure for large deformation where principal directions of strains rotate. In this study, the equivalent strain in large simple shear deformation is re-examined using the Hencky strain. When the amount of simple shear is γ, the equivalent strain of the Hencky strain becomes a logarithmic function of γ, which is the same as the result given by Eichinger [Festigkeitstheoretische untersuchungen, in Handbuch der Werkstoffprüfung, E. Siebel, ed., 2nd ed., Springer, Berlin, 1955, p.715].