How does ALGOR deal with yielding? 1

That is correct.

With a Linear Stress Analysis, Algor (and all FEA programs really) extrapolate the stress/strain curve in the elastic region between 0 and the yield point. Once you exceed the yield stress, it continues along the same slope of the curve to determine stresses at higher strains and/or deflections.

To get accurate results, you need nonlinear material models. I typically run just about everything that I think may exceed yield with bi-linear material models.

--Scott

That is too bad. I believe I only have the option to run with linear materials.

If I upgrade Algor to be able to do this, will it also provide failure analysis?

By "Failure Analysis" do you mean crack propogation? Or just a Von Mises, or other failure criteria comparison? If the former, you need a different type of analysis software. If the latter, the linear stress post-processor has VM stress and others.

Algor non-linear will handle post-yield behavior and permanent deformation.