The Concept of Material Metric in Finite Viscoplasticity

In continuum mechanics the material metric, until now, has been axiomatically regarded as “essentially” Euclidean (either Euclidean or reducible to such by coordinate transformation). In our recent work we have shown the form of the material metric to be related to the internal structure thereby adducing its thermodynamic significance as an internal variable. In this paper we pursue this idea analytically and justify our position by deriving hereditary constitutive equations for finite viscoelasticity, plasticity and viscoplasticity using the concept of intrinsic time. Standard forms follow in the limit of small deformation.