1. Reference problem#

_images/10000200000004530000015FCDEB098627D618FE.png

1.1. Geometry#

Figure 1: Reference problem (for a \(90°\) rotation)

We consider a cubic element of matter with a side of \(1000\mathrm{mm}\) subjected alternately to a tensile force and then to an overall rotation of \(45°\). It undergoes a total of 4 traction/rotation cycles.

1.2. Material data#

Here we consider the elasto-plastic behavior law with isotropic von Mises type work hardening: VMIS_ISOT_LINE. The table below lists the parameters used; in order to reinforce the comparison, the parameters used result in laws of behavior that are identical in both cases (linear isotropic work hardening).

Young’s module:

\(200000\mathrm{MPa}\)

Poisson’s Ratio

\(\mathrm{0,3}\)

Elastic limit

\(200\mathrm{MPa}\)

Linear work hardening module

\(2000\mathrm{MPa}\)

1.3. Boundary conditions and loads#

In modeling \(A\), in \(\mathrm{3D}\) we block the normal movements of the front and rear faces, in order to compare the results to the modeling \(B\) \(\mathrm{2D}\) (D_ PLAN).

In modeling \(C\), also in \(\mathrm{3D}\), the movements of the front and rear faces are left free, in order to compare the results to the modeling \(D\) \(\mathrm{2D}\) (C_ PLAN).

Two types of phases must be distinguished: traction phases and rotation phases.

First traction phase

Entity

Load Type

Value

Underside

FACE_IMPO

\(\mathrm{DNOR}=0\)

Top side

FACE_IMPO

\(\mathrm{DNOR}=\mathrm{500mm}\)

Rotation axis

DDL_IMPO

\(\mathrm{DX}=0\)

Front panel (\(\mathrm{3D}\))

FACE_IMPO

\(\mathrm{DNOR}=0\)

Back side (\(\mathrm{3D}\))

FACE_IMPO

\(\mathrm{DNOR}=0\)

Next pull-ups:

Entity

Load Type

Value

Underside

LIAISON_OBLIQUE

\(\mathrm{DZ}=0\)

Top side

LIAISON_OBLIQUE

\(\mathrm{DZ}=\mathrm{200mm}\)

Side \(X=0\); \(Z=\mathrm{1mm}\)

LIAISON_OBLIQUE

\(\mathrm{DX}=0\)

Rotation axis

DDL_IMPO

\(\mathrm{DX}=\mathrm{0,}\mathrm{DZ}=0\)

Front panel (\(\mathrm{3D}\))

DDL_IMPO

\(\mathrm{DY}=0\)

Back side (\(\mathrm{3D}\))

DDL_IMPO

\(\mathrm{DY}=0\)

Rotation phase:

Boundary conditions

Entity

Load Type

Value

Rotation axis

DDL_IMPO

\(\mathrm{DX}=\mathrm{0,}\mathrm{DZ}=0\)

Front panel (\(\mathrm{3D}\))

DDL_IMPO

\(\mathrm{DY}=0\)

Back side (\(\mathrm{3D}\))

DDL_IMPO

\(\mathrm{DY}=0\) or free

The rotation load is imposed via a macro named CHAR_ROTA; an overall rotation of \(45°\) per phase is imposed, divided into 5 increments of 9°.