Why can you use a Plastic material in a Static study?

Your question doesn't make a lot of sense to me. What do you mean by plastic? A polymer based material or a material that exhibits plasticity - ie it bends and stays bent or maybe something else?

Hi Kevin: I believe you are expressing concern for how plastic materials can behave - namely, the loading can cause deformation beyond linear-elastic behavior. I can think of a few cases where you might want to use a linear-elastic behavior.

In one case we use the linear-elastic run in pragmatic FEA as a method to transition to a nonlinear run. That is, (as we taught the course), we encouraged a philosophy of "...just getting the model to run...", and "...take baby-steps..",  using simple linear-elastic behavior. The turn-around is relatively quick compared to nonlinear, and you can trouble-shoot things like meshing issues, examining behavior due to applied boundary conditions (is the model deforming as expected?), evaluating reaction forces at supports, and so-on. Conversely, I have seen cases where users plow directly into a nonlinear model and uncover scores of issues that are super-difficult to identify - and the turn-around can take a very long time to trouble-shoot since the nonlinear stepping algorithm can take a long time. Only after conducting a linear-elastic run would we encourage setting-up a nonlinear model since the user has presumably fixed any issues and observed some sense of reasonableness in the linear run. 

For a second case I have seen some PVC materials exhibit linearity up to about 3 or 4% strain (esp. at low temperature applications), so a linear-elastic set-up might be appropriate if loading is not expected to cause strain greater than these values.

For a third case I have seen customers who purposely do not want the response of their polymer plastic to "get into" the nonlinear response region. For a given loading, they iterate on geometry, wall thickness, adding ribs and so-on and conduct linear-elastic runs to stay under what they consider their "not-to-exceed" strain (which is usually the "proportional limit" of the stress-strain curve, as you may already know). I have observed this design philosophy for some plastic housing assemblies of portable power tools, for example.

However, I appreciate your comment about a warning from the software. It might be a good idea for the software to post a note to the user that linear-elastic behavior is assumed, should they choose a relatively soft material. However, it might be hard to define a threshold for the notice to appear - a good thought.

Hope that helps a little. - Tony

Kevin, I come to this a bit late.  Plastic ain't linear, that's likely to be the root of the problem. 

Take a look at a normalized stress-strain curve for any polymer (by the way, the differences between rubber and plastic are that plastics come in more colors and rubber starts with an r) and compare it to a normalized curve for any metal.  Here I take normalized to mean that stress is expressed in terms of its value divided by its "yield".  Yield here is in quotes because it is a problematic term for a polymer (beginning with an r or a p).  True stress will also work, and its more entertaining.  When testing a polymer dogbone specimen in tension you'll need to pull it at a much higher rate than for the metal to get anything reasonably comparible.  One more correctly reports the secant modulus for a polymer tension test, not Young's.  Some time when you're really quite boooored, take a look at the Four Element Model of Stress Relaxation and Creep.  'Round bed time would be good.  Oh, and did I mention property's temperature dependance?