The formulation of constitutive equations at large plastic deformations of solids has been the subject of an intense debate since the mid 1960s, when strain decompositions into elastic and plastic parts were largely discussed. Astonishingly, the debate is still active and gives rise to interesting synthetic papers on the subject like the present one. One question is the choice of the proper set of state variables on which constitutive quantities and especially the free energy function should depend.
The author recalls that the total deformation and plastic deformation tensors cannot be regarded as state variables, since they depend on an a priori arbitrary reference configuration. Instead, the set of state variables for describing the elastoplastic and elastoviscoplastic behaviour of solids, are the elastic strain, the temperature and additional internal variables that must be independent of the choice of the reference configuration. Examples of internal variables are hardenig variables describing the isotropic hardening behaviour of metals, for instance. They should, at least in principle, be measurable by a physical mean (one can think about the example of “dislocation density” variables, not mentioned in the text).
The author recasts classical constitutive equations of isotropic elastoplasticity and anisotropic elastoviscoplasticity into the proposed framework where the constitutive functions depend primarily on the proposed set of state variables. The choices of state variables proposed by the author belong in fact to the continuum thermodynamics framework settled by P. Germain, Q. S. Nguyen and P. Suquet [J. Appl. Mech. 50, 1010–1020 (1983; Zbl 0536.73004)] and J. Lemaitre and J. L. Chaboche [Mechanics of Solid Materials (1990; Zbl 0743.73002)]. Regarding anisotropic elastoplasticity, a triad of material vectors, first introduced and called directors by J. Mandel [Int. J. Solids Structures 9, 725–740 (1973; Zbl 0255.73004)], are necessary to formulate properly the theory. Such considerations are helpful for implementing consistent models in numerical schemes in computational mechanics. The analysis is, however, restricted to non-porous materials, but it can be readily extended to compressible plasticity theory.