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On the construction of constitutive equations for large deformations

Herrmann, W.

This paper attempts to give an elementary review of the kinematics of large deformations with a view to illustrating some of the underlying geometric concepts, and then goes on to review some basic features of elastic, hypoelastic, and rate type constitutive equations relevant to their use in numerical methods. Since some recent work has emphasized working in a rotated'' intermediate configuration, one in which the rigid body rotation has been backed out, results relating to this configuration are included, otherwise all of the results have been read off directly from Truesdell and Toupin ( ) or Truesdell and Noll ( ). Finally, results given by Nemat-Nasser ( ) are quoted which reconcile some generalizations of infinitesimal plasticity and some remarks are made relevant to the introduction of tensor internal state variables. Thermodynamic effects, although important in calculations, are omitted to emphasize kinematical effects. Because recent authors have used different names and symbols for stress and strain tensors, it has been found necessary to give a self contained if abbreviated development of the kinematics, which, however, allows a compact discussion of constitutive equations.