Viscoplastic materials non implicit normality rules

Some materials interesting for engineering appplications do not come with scope of generialized standard material (GSM) class for which efficients and robust algorithms are available. Typical examples are constitutive laws geomaterials. Nevertheless, they are not the only ones. For instance, laws describing the behaviour of metals under cyclic loading which are accurately approached by non standard (visco-) plastic laws. The good properties of GSM result from the generalised normality rule and the convexity of the associated pseudo-potential. The concept of bi-potential, introduced by de Saxce, extends the notion of pseudo-potential and enables to write the evolution laws as implicit normality rules. These materials belong to the implicit standard material (ISM) class, of which the GSM class is a subset. The aim of this paper is to show that the visoplastic model with non-linear kinematic hardening proposed by Chaboche et al. belongs to this class of materials. (C) 2000 Academic des sciences/Editions scientifiques et medicales Elsevier SAS.