Hencky strain and logarithmic rates in Lagrangian analysis

Abstract

An hypothesis conjectured independently by Lehmann et al. (1991), Reinhard and Dubey (1995, 1996) and Xiao et al. (1997) takes Hencky strain H=lnV as the strain measure of choice and supposes the existence of a co-rotational rate H• whose components are equivalent to those of the rate of deformation D for all values of stretch V. From this conjecture, they derived the governing spin tensor Z, known today as the logarithmic spin. Applying the same co-rotational rates to both stress and strain ensures consistency within a constitutive construction, even integrability for sufficiently simple models. Their derivations were done in the Eulerian frame of reference. Here their hypothesis is extended to the Lagrangian frame of reference. Adopting mixed tensor fields allows this construction to take on its most simple form.