6. D modeling#
6.1. Characteristics of modeling#
Behavior \(\mathrm{C4}\): non-linear kinematic work hardening (\(\mathrm{II}\)) in \(\mathrm{3D}\). It is modelled in two ways:
or using the VMIS_CIN1_CHAB behavior. All you have to do is then take:
\({R}_{0}={R}_{I}=\mathrm{SIGY}\), \(b=0\), \({C}_{I}=C(T)=(100+\mathrm{1.7.T})(50+\mathrm{2.T})\), \({G}_{0}=D(T)\)
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:
\({R}_{0}={R}_{I}=\mathrm{SIGY}\), \(b=0\), \({\mathrm{C1}}_{I}={\mathrm{C2}}_{I}=C(T)/2\), \({\mathrm{G1}}_{0}={\mathrm{G2}}_{0}=D(T)\)
Temporal discretization: 40 time steps between \(t=\mathrm{0s}\) and \(t=\mathrm{1s}\) and 30 time steps between \(t=\mathrm{1s}\) and \(t=\mathrm{2s}\).
6.2. Characteristics of the mesh#
The mesh includes a HEXA8 mesh.
6.3. Tested sizes and results#
Behavior VMIS_CIN1_CHAB:
Instant (s) |
Plastic deformation by \(Y\) |
Reference |
Aster |
% difference |
|
1 |
|
2.1072 10—03 |
2.11 10—03 |
2.10—03 |
0.14 |
1.26 |
|
4.18947 10—03 |
4.231 10—03 |
4.231 10—03 |
0.99 |
1.98 |
|
4.18947 10—03 |
4.231 10—03 |
4.231 10—03 |
0.99 |
2 |
|
4.12131 10—03 |
4.163 10—03 |
4.12131 10—03 |
1.00 |
Behavior VMIS_CIN2_CHAB:
Instant (s) |
Plastic deformation by \(Y\) |
Reference |
Aster |
% difference |
|
1 |
|
2.1072 10—03 |
2.11 10—03 |
2.10—03 |
0.14 |
1.26 |
|
4.18947 10—03 |
4.231 10—03 |
4.231 10—03 |
0.99 |
1.98 |
|
4.18947 10—03 |
4.231 10—03 |
4.231 10—03 |
0.99 |
2 |
|
4.12131 10—03 |
4.163 10—03 |
4.12131 10—03 |
1.00 |
6.4. note#
The difference with the reference solution (obtained for a very fine temporal discretization) comes from the temporal discretization. Here, a compromise was chosen between reasonable temporal discretization in terms of calculation time and nevertheless fairly accurate.