A bar of length 1 is clamped at the left edge and is subjected
at the right edge to a step velocity of 0.7.
The Young's modulus is 1 and the density is 1.
The velocity induces a stress step of 0.7 in the bar which
travels with a speed of 1 to the left.
At the left edge it re-bounces, and wants to build a stress of 1.4.
The yield stress in plasticity model is 1.
We soften the yield stress with the plasticity parameter .
This maximum stress softens from 1 at
down to 0 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 1.5 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.