1. Introduction

It is a coupling model between behaviors modeling creep, type GRANGER and concrete models modeling plasticity phenomena, either general (Von Mises) or specific to concrete, type BETON_DOUBLE_DP, implemented in the general resolution algorithm of STAT_NON_LINE [R5.03.01].

Existing models are used with the objective of chaining the resolution of the internal equations of the two models during an iterative algorithm, which takes place at each Gauss point, at each iteration. It is therefore a « strong » coupling, since the internal equilibrium equations for creep and plasticity are rigorously satisfied at all times.

This chaining makes it possible to avoid the complete development of a true resolution coupled with creep/plasticity, but has the disadvantage of a higher calculation cost. In fact, at each Gauss point, and at each iteration, it is a principle necessary to solve several times the equilibrium equations for plasticity and those for creep, until the balance between creep and plasticity is obtained. However, this makes it possible to couple a law of creep, with any law of plasticity, for a moderate development cost. On the other hand, in the case of law BETON_DOUBLE_DP, in post-peak traction, the work-hardening curve is linear, and the local resolution algorithm converges in a single iteration. The calculation cost therefore remains limited.

The combinations available by this method are, in the version of Code_Aster relating to this document:

• for the law of creep: GRANGER_FP, GRANGER_FP_V, GRANGER_FP_INDT

• for the law of plasticity: ELAS, VMIS_ISOT_LINE, VMIS_ISOT_TRAC,,,, VMIS_ISOT_PUIS, ROUSS_PR, BETON_DOUBLE_DP

Note: the coupling between the creep law BETON_UMLV_FP and the damage law MAZARSet ENDO_ISOT_BETON is in fact a law of behavior written specifically to take into account the coupling between these two models, which does not fall under the principle described in this document. This coupling is described in R7.01.06.