Issue 70
A. Baryakh et alii, Frattura ed Integrità Strutturale, 70(2024) 191-209; DOI: 10.3221/IGF-ESIS.70.11
trial R
e
1 ( , n ) n m A 1
D N 0
1
R
(42)
0
t
(
)
A
y
Now the Jacobian is represented as
P
I
1
1
(43)
1 1 y 1
m
J
N
1 T
m
t
Such form of the tangent operator of the system of residuals is possible to be determined from the initial approximation = 0. Nevertheless, it should be noted that the Jacobian is undetermined on the yield surface. Thus, the solution of the system might be unstable as the stress tensor approaches the yield surface as well as at small values of the parameter m . In the second case when the stress tensor is related to an edge of the Mohr-Coulomb yield surface, the system of residuals is written in a similar way trial 1 1 2,6 2,6 D N N 0 e n R
1
m
( , n
)
A
1
1
0
R
1
(44)
t
(
)
A
y
1
m
( , n
)
A
2,6
2,6
R
0
t
(
)
A
2,6
y
The corresponding Jacobian is
P P
I
1
2,6
1
1 1 y 1
m
N
1 T
0
m
t
(45)
J
1
2,6
m
1
2,6 N 0 T
m
t
y
2,6
The results of multivariant numerical simulation of the creep of salt specimens are shown in Fig. 6. The corresponding calibrated parameters of the elastic-viscoplastic model are given in Table 5.
Young's modulus, GPa
Poisson's ratio
Cohesion, MPa
Frictional angle, degree.
Dilatancy angle, degree
Viscosity, hour
Rate sensitivity
Load level
0.3 0.4 0.5 0.6 0.7 0.8
1.5 1.5 1.5 1.5 1.5 1.5
0.3 0.3 0.3 0.3 0.3 0.3
1.7 1.7 1.7 1.7 1.7 1.7
30 30 30 30 30 30
18 18 18 18 18 18
3.5·10 3
0.4 0.4 0.4 0.4 0.3 0.3
10 4 10 4
1.6·10 4 2.2·10 4 2.8·10 4
Table 5: “Mohr-Coulomb + Perzyna” model parameters
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