A bar of length
is clamped at the left edge and is subjected
at the right edge to a step velocity of
.
The Young's modulus is
and the density is
.
The velocity induces a stress step of
in the bar which
travels with a speed of
to the left.
At the left edge it re-bounces, and wants to build a stress of
.
The yield stress in plasticity model is
.
We soften the yield stress with the plasticity parameter
.
This maximum stress softens from
at
down to
at
.
To prevent unlimited localization of the plasticity zone, viscoplasticity is used,
so that stresses a bit above the yield stress are allowed.
With 64 linear elements we find after time
the following result for the stress:
Notice that the stress is a bit higher then 1, which is due to the viscoplastic law.
The result for
is:
The plasticity occurs over a length larger then the element size. Without viscoplasticity, the plasticity would have localised to 1 element, because of the softening.