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

\(\mathrm{EPYY}\)

2.1072 10—03

2.11 10—03

2.10—03

0.14

1.26

\(\mathrm{EPYY}\)

4.18947 10—03

4.231 10—03

4.231 10—03

0.99

1.98

\(\mathrm{EPYY}\)

4.18947 10—03

4.231 10—03

4.231 10—03

0.99

2

\(\mathrm{EPYY}\)

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

\(\mathrm{EPYY}\)

2.1072 10—03

2.11 10—03

2.10—03

0.14

1.26

\(\mathrm{EPYY}\)

4.18947 10—03

4.231 10—03

4.231 10—03

0.99

1.98

\(\mathrm{EPYY}\)

4.18947 10—03

4.231 10—03

4.231 10—03

0.99

2

\(\mathrm{EPYY}\)

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.