Animations of elastic-plastic rings crushed between rigid plates.



Please consult "Crushing of an Elastic-Plastic Ring Between Rigid Plates with and without Unloading" by Tim McDevitt and Jim Simmonds for an explanation of the notation used below.

Scenario I

In Scenario I, the beam is originally straight and is bent elastically into a circular ring. It is then crushed between two rigid plates. Green indicates parts of the ring which are elastic and red (loading) and blue (unloading) indicate which parts are plastic. (mu=0.8,lambda=10^-6)

Since the ring was originally straight, it "wants" to straighten along the plates. So most of the stress is concentrated near the "sides". Since lambda is almost zero, we see what look like plastic hinges forming on both "sides" as the load (nu) becomes relatively large.
 
 



Scenario II

This ring is stress-free in the circular configuration. Green indicates parts of the ring which are elastic and red (loading) and blue (unloading) indicate which parts are plastic. (mu=5,lambda=0.1)

It is difficult to tell, but the ring first yields (turns red) at the contact points with the plates and then on the "sides". Eventually, an unloading (blue) zone extends from the elastic region toward the "hinge" location. Note that since lambda is fairly large, a true hinge does not form. Also, note how much more force is required (nu) in this case as opposed to Scenario I.
 
 



Scenario III

Scenario III is very similar to Scenario I, except that the intially straight beam is bent plastically into a ring and then crushed. In this scenario, there are no elastic (green) regions. Also note that the ring begins to unload (blue) immediately. (mu=5,lambda=0.1)
 
 



Comparison between Scenario II and Scenario III

Side by side comparison of a Scenario II and a Scenario III ring. At first, the II ring is stiffer because it is entirely elastic. Then, when the plastic (loading) zones suddenly appear, the ring collapses rather quickly. In contrast, a III ring always has a plastic (loading) zone, thereby making it less stiff initially. However, no sudden changes occur to cause rapid crushing. (mu=20,lambda=0.01)