Keywords: elasticity, damage, non linear behaviour, concrete, finite element, numerical aspects.

An effect of the nucleation and growth of microvoids and/or microcracks (damage) on the overall response behavior of a wide class of materials is now clearly inderstood. The material damage of occurs when atomic bonds break at the microstructural level. These microscopic alterations react upon the macroscopic thermomechanical materials properties: elastic softening, decreased conductictivity, plastic yield surface alteration, etc.

For concrete, the experimental behaviour analysis (concrete is assumed initially isotropic) let us say the principal following phenomena:

• a loss of stiffness beyond a certain stress point due to damage which is strongly anisotropic due the directionality of the defects (induced anisotropy);
• a permanent or irreversible strains with the loss of material stiffness (which are due to the growth of damage);
• a stiffness recovery with the change from the damaging loading in traction to a compression loading called "unilateral behaviour" (the damage can be active or inactive, when the microcracks are respectively open or closed);
• an asymmetric behaviour between traction and compression and a softening behavior during traction and compression.

In many engineering situations, concrete can be considered as an elastic material susceptible to damage. Continuum damage mechanics (CDM) is intended to interpret and describe the phenomena connected with the deterioration of materials before the macroscopic rupture. However, the behaviour of this material is of most complexes and its modelling can generate numerous variables. In this survey we present a local simple model of anisotropic damage, to translate phenomena of deterioration of the concrete. We endeavoured to describe the damage by one single variable, making the call that restricts intrinsic parameters of the material easily accessible by the experimentation [1,2].

1

Y. Labadi, N.E Hannachi, "Non linear damage behaviour of concrete structures", Can. J. Civ. Eng., Vol. 32, 765-774, 2005. doi:10.1139/l05-018

2

Y. Labadi, N.E Hannachi, "Numerical simulations of brittle damage in concrete specimens", Strength of Materials, Vol. 37, No. 3, Springer Science & Business Media, Inc., 2005. doi:10.1007/s11223-005-0039-5

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