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F
x
1
l
F
l
Case a:
σ
1
T
> 0
Case b:
σ
1
T
< 0
Figure 2.8.
Explanatory scheme of an orientation of a contact force leading
to values of
σ
11
Τ
,
positive and negative respectively
The numerical simulation performed by Yunus [YUN 08, YUN 10] clearly
showed that, for the same stress state, the orientation of contact forces depends
strongly on the loading history. Indeed the numerical simulation of semi-alternated
cyclic loadings with isotropic stress at the end of each cycle leads to values of
σ
1
T
σ
1
N
which, for the maximum values of the deviatoric stress, are positive and increase
significantly with the applied cycles and are negative when the stress state is equal
to an isotropic state (except for the initial state, for which this value is equal to zero).
Figure 2.9 clearly shows an evolution of the orientations of the contact forces
throughout the cyclic loading in agreement with the local mechanisms described by
Jean Biarez in his thesis [BIA 62].
0,002
30
3
0 50
20
2 10
1
20
0,001
10
0
0
-0,001
0
0,5
1
1,5
2
2,5
0
0 , 5
1
1 , 5
2
2 , 5
Déformation axiale (%)
Axial strain (%)
Axial strain (%)
D é formation axiale (%)
Figure 2.9.
Analysis of the evolution of the orientations of contact
characterized by the ratio
σ
1
T
σ
1
N
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