1. Introduction

The Drucker-Prager law makes it possible to model in an elementary way the elasto-plastic behavior of concrete or certain soils. Compared to Von-Mises plasticity with isotropic work hardening, the difference lies in the presence of a term in \(\mathrm{Tr}(\sigma )\) in the formulation of the threshold and a non-zero spherical component of the plastic deformation tensor.

In Code_Aster, the law exists in the associated version (DRUCK_PRAGER) and the non-associated version (DRUCK_PRAG_N_A), which is more suitable for certain soils because it allows dilatance to be better taken into account.

This note brings together the theoretical aspects of several developments made in the code around this law: its integration according to an implicit time pattern, a Rice location indicator and the calculation of sensitivity by direct differentiation. The material is assumed to be isotropic. The Rice indicator and the sensitivity calculation do not work under the assumption of plane constraints.

The theory and developments have been made for three types of work hardening functions: linear, parabolic, and exponential (DRUCK_PRAG_N_A only). In linear and parabolic cases, this function is in all cases constant beyond an « ultimate » cumulative plastic deformation.