For a simple uniaxial compression test, the reported stresses are not continuous. It seems as though local unloading occurs. This is physically not correct. For parameters psi<1, the surface is not convex anymore! This is also unphysical. See attached PDF. Is this a code defect?

It is not a defect.
(1) Yes. Yield surface can be nonconvex at the ratios below some values. Consider Fig 4.11 of Theory Manual (with psi<0.80).
(2) Drucker's postulate on Convex requirement is only for materials with hardening.
(3) Non-convexity doesn't automatically mean "unphysical"; non-convexity is physical for materials with softening behaviors.
(4) Indeed, there are some lode angle dependence models (like William and Warnkle (1975)) which do satisfy convexity for all Lode angle beta.
a: they are too complex. Argyris (1974) proposed a simpler one but it loses convexity. The one ANSYS proposed is similar to Argyris.
b: for ratios close to 0.5, even convexity models are available. Currently, there are no robust numerical algorithms to handle them due to their non-smoothness (corners). You can not get any converged solutions.
(5) We try to get more robustness at the price of weakening the convex requirement (for non-softening materials). This is the reason we use Argyris-type model.

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