Code_Aster ®
Version
6.4
Titrate:
SSNL120 - Cyclic Réponse of the law of behavior of the concrete
Date:
16/07/03
Author (S):
S. GHAVAMIAN, L. DAVENNE, F. GATUINGT Key
:
V6.02.120-A Page:
1/6

Organization (S): EDF-R & D/AMA, LMT Cachan

Handbook of Validation
V6.02 booklet: Nonlinear statics of the linear structures
Document: V6.02.120

SSNL120 - Cyclic Réponse of the law
of behavior of the concrete (model of Borderie)

Summary:

In this example one tests the model of behavior of the concrete of Borderie [R7.01.07] in his version 1D
using a multifibre element of beam [R3.08] under axial stress. The loading is composed of
traction with loading and unloading followed by compression also with loading and unloading. It
allows to test resistances in traction and compression, to highlight the phenomenon of
refermeture of fissures and to test the anelastic deformations.
Handbook of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/03/008/A

Code_Aster ®
Version
6.4
Titrate:
SSNL120 - Cyclic Réponse of the law of behavior of the concrete
Date:
16/07/03
Author (S):
S. GHAVAMIAN, L. DAVENNE, F. GATUINGT Key
:
V6.02.120-A Page:
2/6

1 Characteristics
general

1.1 Geometry

Beam comforts length unit, of square section on side unit:

y
X
y
1 m
With
B
Z
1 m
1 m


1.2
Material properties

Young modulus: E = 2. 1010 Pa
Resistance in traction: Rt = 4. 106 Pa
Resistance in compression: Rc = 40. 106 Pa

1.3
Boundary conditions

Embedding in a: dx = Dy = dz = 0 and X-ray = ry = rz = 0.

1.4 Loadings

One decreases to grow and the axial deformation (via a displacement imposed out of B
according to X) according to the following sequence:

Moment Deformation
0 0,0
1 1,4.10­4
2 0,5.10­4
3 1,0.10­3
4 ­ 4,0.10­3
5 ­ 2,0.10­3
6 ­ 5,0.10­3
7 0,0

2
Reference solution

The reference solution is the uniaxial response of the model for the parameters selected materials.
This solution was obtained using the code Eficos (code with multi-layer beams 2D [bib1]) in
which this law was established.

3 Bibliography

[1]
GHAVAMIAN HS., MAZARS J.
: Strategy of calculations simplified for the analysis of
behavior of the reinforced concrete structures: code EFICOS. French review of civil engineering
1998; 2: 61-90.
Handbook of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/03/008/A

Code_Aster ®
Version
6.4
Titrate:
SSNL120 - Cyclic Réponse of the law of behavior of the concrete
Date:
16/07/03
Author (S):
S. GHAVAMIAN, L. DAVENNE, F. GATUINGT Key
:
V6.02.120-A Page:
3/6

4 Modeling
With

4.1
Characteristics of modeling A

Longitudinal grid of the beam:
We have 2 nodes and 1 element (POU_D_EM).

With
B


The concrete part of the cross section of the beam is with a grid (AFFE_SECT) by 4 fibers:



Note:

The problem being 1D, only one fiber could seem sufficient, but that would lead to
to have null terms in the matrix of rigidity (the own inertia of fibers not being taken
in account) and with an error at the time of the solution of the system of equations.

The concrete is modelled with the model of damage of Christian Borderie in version 1D
(LABORD_1D) [R7.01.07]. The parameters material used are as follows:

Y01 = 310 Pa
Y02 = 7000 Pa
A1 = 9,0.10-3 Pa-1
A2 = 5,2.10-6 Pa-1
B1 = 1,2
B2 = 2,0
1 = 106 Pa
2 = - 40.106 Pa
F = - 3,5.106 Pa
Handbook of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/03/008/A

Code_Aster ®
Version
6.4
Titrate:
SSNL120 - Cyclic Réponse of the law of behavior of the concrete
Date:
16/07/03
Author (S):
S. GHAVAMIAN, L. DAVENNE, F. GATUINGT Key
:
V6.02.120-A Page:
4/6

4.2 Functionalities
tested

Commands



AFFE_MODELE GRID



AFFE
TOUT
“OUI”
PHENOMENE
“MECANIQUE”
MODELISATION
“POU_D_EM”
DEFI_MATERIAU
“ELAS”


“LABORD_1D'
AFFE_MATERIAU
GROUP_MA


MATER
AFFE_CARA_ELEM BEAM
GROUP_MA



SECTION

ORIENTATION
GROUP_MA


CARA
“ANGL_VRIL”
AFFE_SECT
GROUP_MA


MAILLAGE_SECT


TOUT_SECT
“OUI”

GROUP_MA

MODEL AFFE_CHAR_MECA



DDL_IMPO
GROUP_NO
MODEL STAT_NON_LINE



CHAM_MATER


CARA_ELEM


EXCIT
CHARGE


FONCT_MULT

COMP_INCR
LABORD_1D

NEWTON
MATRICE
“TANGENTE”
CALC_NO OPTION

“REAC_NODA”

REUSE
RESULTAT
CHAM_MATER
CARA_ELEM
EXCIT
CALC_ELEM OPTION

“DEGE_ELNO_DEPL”

REUSE
RESULTAT
MODELE
CHAM_MATER
CARA_ELEM

Handbook of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/03/008/A

Code_Aster ®
Version
6.4
Titrate:
SSNL120 - Cyclic Réponse of the law of behavior of the concrete
Date:
16/07/03
Author (S):
S. GHAVAMIAN, L. DAVENNE, F. GATUINGT Key
:
V6.02.120-A Page:
5/6

5
Results of modeling A

The stress-strain curve is represented on the figure below:

5,0
0,0
- 5,0
- 4,0
- 3,0
- 2,0
- 1,0
0,0
1,0
- 5,0
- 10,0
- 15,0
- 20,0
- 25,0
- 30,0
- 35,0
- 40,0
- 45,0
Deformation (x1000)


One tests the constraints obtained for the deformations imposed on the moments indicated in
paragraph [§1.4]:

Moment Reference Aster
Relative error %
1 1,707816
106 1,707816
106 <
10­3
2 0,247022
106 0,247022
106 <
10­3
3 0,068862
106 0,068862
106 <
10­3
4 ­ 22,2404
106 ­ 22,2404
106 <
10­3
5 ­ 2,14356
106 ­ 2,14356
106 <
10­3
6 ­ 16,3512
106 ­ 16,3512
106 <
10­3

One also tests the maximum constraints (traction and compression) and the deformations
corresponding

Peaks in constraint
Reference
Aster
Relative error %




Traction



Constraint
3,86138 106
3,86138 106
< 10­3
Deformation
1,036 10­4
1,036 10­4
< 10­3




Compression



Constraint
­ 40,9496 106
­ 40,9496 106
< 10­3
Deformation
­ 1,810-3
­ 1,810­3
< 10­3


Handbook of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/03/008/A

Code_Aster ®
Version
6.4
Titrate:
SSNL120 - Cyclic Réponse of the law of behavior of the concrete
Date:
16/07/03
Author (S):
S. GHAVAMIAN, L. DAVENNE, F. GATUINGT Key
:
V6.02.120-A Page:
6/6

6
Summary of the results

The results obtained with Code_Aster are in very good agreement with those of code EFICOS.

Handbook of Validation
V6.02 booklet: Nonlinear statics of the linear structures
HT-66/03/008/A

Outline document