Example 14: Continuous metal forming.

A metal sheet is extruded in a continuous process. The initial thickness of the metal is 1, and the thickness after extrusion is 0.9. The Young's modulus is $7000$ and the Poisson ratio is $0.2$. The Von Mises plasticity model is used to model permanent deformations (yield stress $24.3$). The first flow shows the finite elements mesh:

The extrusion is modeled by prescribing a velocity $1.0$ at the right edge of the computational domain. On the left edge, the stresses and plastic strains are set to zero, in order to specify that virgin material enters the domain. Friction at the upper wall is not taking into account in this example. The result for $\kappa$, measuring the build up of plastic strains, is plotted below