1. Reference problem#

1.1. Geometry#

We consider a cube with side \(3\,{mm}\).

1.2. Material properties#

The material is elasto-plastic with linear isotropic work hardening (VMIS_ISOT_LINE) whose properties are:

  • Modulus of elasticity: \(E=210000\,{MPa}\)

  • Poisson’s ratio: \(\nu =0.3\)

  • Linear work hardening module: \(H=100\,{MPa}\)

  • Elastic limit: \({\sigma }_{y}=100\,{MPa}\)

  • Thermal conductivity: a function of the temperature in the figure

  • Volume heat: a function of the temperature in the figure

_images/100002010000022E0000019D72B15F1859CF2C82.png

Fig. 1.1 Thermal conductivity#

_images/100002010000022E0000019DB10A84CBD51D37C6.png

Fig. 1.2 Volume heat#

1.3. Boundary conditions and loads#

1.3.1. Thermal calculation#

A radiation condition is imposed on five sides of the cube (see figure). v1.01.395-fig-rayonnement) with:

  • Boltzman constant: \({5,67}\times {10}^{-14} J \, {{mm}}^{-2} \, {K}^{4}\);

  • emissivity: \(0,75\)

  • outside temperature: \(20°C\)

_images/1000000000000423000002E37275065166D3E4F0.png

An exchange condition on the top side (see figure v1.01.395-fig-echange) with:

  • Exchange coefficient: \({1,0} \, W\,{{mm}}^{-2}\,{K}^{-1}\)

  • Outside temperature: a function of the weather in figure v1.01.395-fig-temperatureExte

_images/1000000000000423000002E3A26C9C3EE7CC0521.png
_images/100002010000022E0000019DD02210247C1E7701.png

An exchange condition on the other sides (see figure) with:

  • Exchange coefficient: \({1,5}\times {10}^{-5}\, W \, \,{{mm}}^{-2}\,{K}^{-1}\)

  • Outside temperature: \(20°C\)

1.3.2. Mechanical calculation#

On the lower surface (see figure 6 v1.01.395-fig-surfaceEncastrement), we impose \(DX=DY=DZ=0\).

On five sides of the cube (see figure), pressure \(p=1000\,{MPa}\) is imposed

_images/1000000000000432000002E3D257BB742C66BCDF.png

: name: v1.01.395 - FIG-Surface mounting

Surface for embedding

1.4. Initial conditions#

Nil. -