1. Reference problem

1.1. Modeling geometry A

An axisymmetric bar of radius \(\mathrm{1mm}\) and height \(\mathrm{10mm}\) subjected to a simple tensile test (with imposed displacement) is considered. This test is chosen because it makes it possible to obtain uniform mechanical fields.

Figure 1.1: Axisymmetric bar.

1.2. Modeling geometry B

Here we consider a cube with side \(\mathrm{1mm}\) subjected to traction.

The front face is blocked in direction \(\text{X}\), the left face in direction \(\text{Y}\), the bottom face in direction \(\text{Z}\) and an incremental pull of \(\mathrm{0,001}\text{mm}\) is applied to the upper face.

1.3. Material properties

The material is perfect elastoplastic with a Young’s modulus of \(300000\text{MPa}\), a Poisson’s ratio of 0 and an elastic limit of \(300\text{MPa}\).

1.4. Boundary conditions and loads

For modeling A, 5 traction increments of \(\mathrm{0,01}\text{mm}\) are carried out, so that the total deformation increment is \(1.0\text{E-3}\) and the elastic limit is reached at the first step.

For modeling B, the front face is blocked in direction \(\text{X}\), the left face in direction, the left face in direction \(\text{Y}\), and an incremental pull of \(\mathrm{0,001}\text{mm}\) is applied to the upper face. \(\text{Z}\)

The temperature varies linearly in the bar from \(\text{O°C}\) to \(\text{5O°C}\) over the 5 time steps.

In order to test the various possibilities offered by the macro-command CALC_BORDET, when possible, parameters that depend on the temperature and the plastic deformation rate are used. The list of parameters used is shown in the table below.

Parameter	Type	Value
M	Scalar	22
SIG_CRIT	Scalar	250
VOLU_REFE	Scalar	1
SIGM_REFE	Function	\(200+\text{T}\)
SEUIL_CALC	Tablecloth	\(\{\begin{array}{cc}10T& \text{si}{\dot{\stackrel{ˉ}{\varepsilon }}}^{p}=\mathrm{0,0005}\\ 5T& \text{si}{\dot{\stackrel{ˉ}{\varepsilon }}}^{p}=\mathrm{0,001}\end{array}\)
DEF_PLAS_REFE	Scalar	0

Table 1.1 : Bordet parameters used