1. Introduction

1.1. Global models

A so-called global plate or structural element behavior model, in general, means that the law of behavior is written directly in terms of the relationship between generalized stresses and generalized deformations. The global approach to modeling the behavior of structures applies in particular to composite structures, for example reinforced concrete (see Figure), and represents an alternative to so-called local or semi-global approaches, which are finer but more expensive models (see [bib5] and [bib6]). In the local approach, fine modeling is used for each of the phases (steel, concrete) and their interactions (adhesion) and in the semi-global approach, the slenderness of the structure is exploited to simplify the description of the kinematics, which results in models PMF (Multi-Fiber Beam) or multi-layer shells.

The advantage of the global model lies in the fact that the corresponding finite element only requires one integration point in the thickness and especially in obtaining homogenized behavior. This advantage is even more important in reinforced concrete analysis, since the location problems encountered when modeling unreinforced concrete are bypassed. Obviously, a global model represents local phenomena in a crude way and requires more validation before it can be applied to industrial examples.

Figure 1.1-a : Reinforced concrete slab.

1.2. Objectives of the GLRC_DM law

Model GLRC_DM is capable of representing the damage to a reinforced concrete plate, when this one remains limited, that is to say without reaching the break. It was inspired by the GLRC_DAMAGE model and is complementary to it. While GLRC_DAMAGE can also represent damage, this is only possible for flexural loading without any impact on membrane behavior. On this point GLRC_DM is more faithful to physics, but unlike GLRC_DAMAGE it does not allow plasticity to be taken into account. By being simpler, GLRC_DM is also more efficient in terms of calculation cost and numerical robustness.

The aim is to have identical behavior in the directions \(\mathrm{Ox}\) and \(\mathrm{Oy}\); in addition, the upper and lower reinforcement layers are assumed to be identical.