1. Reference problem#

1.1. Geometry#

Volume element materialized by a square plate \(\mathrm{ABCD}\) with a unit side \(1\mathrm{mm}\):

\(E={2.10}^{5}\mathrm{MPa}\), \(\nu =0.3\), \(\alpha ={2.10}^{5}°{C}^{-1}\)

The material is elastoplastic with linear kinematic work hardening:

\(\sigma =\pm {\sigma }_{y}(T)+C(T){\varepsilon }^{p}\)

\(\mathrm{SIGY}=200.-\mathrm{1.7.T}\) (in \(\mathrm{Mpa}\))

Work hardening module D_ SIGM_EPSI = \(C(T)=1000+\mathrm{2990.T}\) (in \(\mathrm{MPa}\))

Such that the state of stress and deformation are uniform in the volume element:

Point \(A\) stuck in \(x\) and \(y\).

\(\mathrm{DY}=0\) out of \(\mathrm{AB}\)

Force distributed over \(\mathrm{CD}\): \(\mathrm{Fy}\)

Uniform temperature \(T\) out of \(\mathrm{ABCD}\). The reference temperature is \(0°C\).

\(\mathrm{Fy}\) and \(T\) vary over time as follows: