2. Modeling A#

2.1. Characteristics of modeling#

The modeling is two-dimensional with plane deformations D_ PLAN and static non-linear.

The horizontal displacement imposed on the upper facet varies between \(0\) and \(-1\mathit{mm}\) in \(100\) time steps between \(t=0.\) and \(t=10\). The automatic subdivision of the time step is activated to manage situations of non-convergence of local integration.

2.2. Tested sizes and results#

The solutions are calculated at point \(C\) for orthotropic material and compared to code_aster modeling with isotropic material. They are given in terms of stress \({\mathrm{\sigma }}_{\mathit{xy}}\), total volume deformation \({\mathrm{\epsilon }}_{v}\) and isotropic work-hardening coefficients \(\left({r}_{\text{ela}}^{\text{iso},m}+{r}_{\text{iso}}^{m}\right)\) and deviatory \(\left({r}_{\text{ela}}^{d,m}+{r}_{\text{dev}}^{m}\right)\), and summarized in the following tables:

\({\mathrm{\sigma }}_{\mathit{xy}}(\mathit{kPa})\)

\(t\)

TYPE

ISOTROPE

Tolerance (%)

10.0

“AUTRE_ASTER”

-9.905E+03

0.1

\({\mathrm{\epsilon }}_{V}=\text{trace}\left(\mathrm{\epsilon }\right)\)

\(t\)

TYPE

ISOTROPE

Tolerance (%)

10.0

“AUTRE_ASTER”

-6.604E-05

0.1

\(\left({r}_{\text{ela}}^{d,m}+{r}_{\text{dev}}^{m}\right)\) (Map \(\mathit{YZ}\))

\(t\)

TYPE

ISOTROPE

Tolerance (%)

10.0

“AUTRE_ASTER”

1.69732E-02

0.1

\(\left({r}_{\text{ela}}^{d,m}+{r}_{\text{dev}}^{m}\right)\) (Map \(\mathit{XY}\))

\(t\)

TYPE

ISOTROPE

Tolerance (%)

10.0

“AUTRE_ASTER”

1.43123E-01

0.1

\(\left({r}_{\text{ela}}^{\text{iso},m}+{r}_{\text{iso}}^{m}\right)\)

\(t\)

TYPE

ISOTROPE

Tolerance (%)

10.0

“AUTRE_ASTER”

1.00107E-01

0.1