5. C modeling#
5.1. Characteristics of modeling#
Behavior \(\mathrm{C3}\): non-linear kinematic work hardening (\(I\)) in \(\mathrm{3D}\). It is modelled in two ways:
or using the VMIS_CIN1_CHAB behavior. All you have to do is then take:
\({R}_{0}={R}_{I}=\mathrm{SIGY}\), \(b=0\), \({C}_{I}=C(T)=(100+\mathrm{1.7.T})(50+\mathrm{2.T})\), \({G}_{0}=50\)
or using behavior VMIS_CIN2_CHAB, by choosing the parameters in such a way that the two kinematic variables are identical: All you have to do is then take:
\({R}_{0}={R}_{I}=\mathrm{SIGY}\), \(b=0\), \({\mathrm{C1}}_{I}={\mathrm{C2}}_{I}=C(T)/2\), \({\mathrm{G1}}_{0}={\mathrm{G2}}_{0}=50\)
Temporal discretization: 20 time steps between \(t=\mathrm{0s}\) and \(t=\mathrm{1s}\) and 60 time steps between \(t=\mathrm{1s}\) and \(t=\mathrm{2s}\).
5.2. Characteristics of the mesh#
The mesh includes a HEXA8 mesh.
5.3. Tested sizes and results#
Behavior VMIS_CIN1_CHAB:
Instant (s) |
Plastic deformation by \(Y\) |
Reference |
Aster |
% difference |
|
1 |
|
2.1072 10—03 |
2.113 10—03 |
2.1072 10—03 |
0.27 |
1.26 |
|
4.0729 10—03 |
4.0875 10—03 |
4.0729 10—03 |
0.36 |
1.98 |
|
4.0729 10—03 |
4.0875 10—03 |
0.36 |
|
2 |
|
4.0372 10—03 |
3.978 10—03 |
4.0372 10—03 |
1.46 |
Behavior VMIS_CIN2_CHAB:
Instant (s) |
Plastic deformation by \(Y\) |
Reference |
Aster |
% difference |
|
1 |
|
2.1072 10—03 |
2.113 10—03 |
2.1072 10—03 |
0.27 |
1.26 |
|
4.0729 10—03 |
4.0875 10—03 |
4.0729 10—03 |
0.36 |
1.98 |
|
4.0729 10—03 |
4.0875 10—03 |
0.36 |
|
2 |
|
4.0372 10—03 |
3.978 10—03 |
4.0372 10—03 |
1.46 |
5.4. note#
The difference with the reference solution comes from temporal discretization. By refining further, the solution is closer to the analytical solution. A compromise was chosen between reasonable temporal discretization in terms of calculation time and nevertheless fairly accurate.