Issue 67

D. Fellah et alii, Frattura ed Integrità Strutturale, 67 (2014) 58-79; DOI: 10.3221/IGF-ESIS.67.05

 Verify the accounting of the deformations in the matrix phase

N =?< > ε

ε

NM

M

 If yes, no more iterations on this pseudo grain .  Otherwise, perform a new iteration with

NM NM < > = ε ε

 After convergence, we determine the secant homogeneous stiffness G i sct

hom C of the pseudo grain with Mori Tanaka

model:

sct sct = +f ( hom NM i

sct

sct

sct -1 S C C NM Esh NM i ( ) : (

sct

sct

-1

-

) :[ +f I

-

)]

C

C C C

C

i

NM

NM

G i

 Calculate the secant modulus of the RVE and the macroscopic stress.

N

i=1 = f 

sct

sct

C

C

hom

Gi hom

G i

c

o t

= s h m : Σ C E

I DENTIFICATION M AZARS LAW

F

rom the experimental test on the concrete specimen, we aim to identify the needed parameters of Mazar’s model applied to the new mortar. In our analysis, we suppose that all the aggregates introduced in the mortar to prepare the whole concrete remain elastic in all the compressive loading paths. As detailed in the previous section, the parameters of the Mazars model are NM NM NM c c D A , B ,  . As suggested in this law, these parameters fluctuate from reasonable values as stated in Mazars’s model identified in our algorithm as a constraint as:

NM c 1000< B <2000 ,

NM c 1< A <2 ,

-5 NM -4 D 10 < <10 

The optimization of these parameters involves utilizing a simplex algorithm implemented in Matlab code. The objective is to minimize the residual error between the numerical stress obtained from the homogenization model and the experimental stress depicted in Fig.5. The residual error is calculated using the following equation:

2

N  i=1

1





  σ ε (i) - exp

 

 

hom

NM NM NM



er R =

ε (i),A ,B , ε

(27)

11

c

c

D

N

with: er R : Total error. exp σ : Experimental stress at loading direction. hom 11  : Numerical stress estimated by the homogenization model at loading direction, depending on imposed deformation loading ε (i) and the model parameters NM c A , NM c B and NM D ε . N: Number of loading step.

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