Strain measures in continuum mechanics according to the Hill-Seth formula

Abstract

In this article the class of strain measures in continuum mechanics proposed by R.Hill and B.R.Seth is considered. It is used to the derivation of usual strain measures: Green-Lagrange, Almansi-Euler, Biot, and the logarithmic strain by Hencky. The rates of strain are also derived as well as the corresponding stress measures. The results are illustrated with two simple examples: bar in tension and simple shear.