PSI - Issue 37

Sonia Djenad et al. / Procedia Structural Integrity 37 (2022) 321–329 Djenad et al / Structural Integrity Procedia 00 (2019) 000 – 000

324 4

3. Numerical simulation In this section, we emphasize the improvement in compressive strength of confined concrete members. In addition, a numerical model based on finite element analysis was developed and validated to predict the full axially response under imposed monotonic compression loading. It enables us to measure the differences in strengths between unconfined and confined concrete and to draw the preliminary conclusions. 3.1. Materials laws and modeling Concrete behavior is considered as one of complicated material to modelling, this is due to different response in compression and tension and non-linear stress-strain laws with hardening and softening phases (Kezmane et al, 2016). Indeed, in this study, an elastoplastic based-damage model is used to describe the nonlinear material properties of concrete. The concrete damaged plasticity (CDP) model was developed by (Lubliner and al, (1989) Onate and al, (2001)) and elaborated by (Lee and Fenves, 1998). The used concrete model which provides a general capability for the analysis of concrete structures under static or dynamic and cyclic or monotonic loading, is started from an additive strain rate decomposition in elastic and plastic parts el pl = + ε ε ε . The stress-strain relation is given in a matrix form by: ( ) ( ) ( ) 0 1 : : el pl el pl d D D      = − − = − (1) Three stepwise defined material functions describe the stress-strain behavior under uniaxial compressive loading. The compressive damage value is linked to the plastic strain. In the case of simple tension, the stress-strain relationship is linear elastic until the value of the breaking stress is reached. Beyond that, this relationship is written as follows:

( ) 1 ( / ) w

w

t 

2 c c w w

−

 = +

3 c w w e 

3 (1 )

c

−

1 c e

− +

(2)

2





1

c

f

w

t

c

Where c1 = 3, c2 = 6,93: a product of inelastic strain and length parameter. The elastoplastic damage model requires values for material failure ratios and for a tension stiffening parameter. Table. 2 shows the mechanical parameters of the used concrete model.

Table 2. Mechanical parameters of the used CDP model (P. Mark and M. Bender, 2010) Proprieties Values c f Compressive stress (Mpa) 25 ce f Yield stress on compression (Mpa) 7.5 t f Yield stress on tension (Mpa) 2.1 c E Young Modulus (Mpa) 32165  Poisson's ratio 0.2  Angle de dilatation (°) 32 f a Ratio of biaxial to uniaxial strength 1.16 c w max crack opening (µm) 180 w Smeared over average element length (µm) 0 - 180 G Crushing energy on tensile (N.µm -1 ) 25.1 e a Parameter of the flow potential 0.1

The elastic behaviours of the GFRP fabric and adhesive resign are experimentally determined by (Si Salem et al,