Whenever departing from a pure reversibility in models that are relevant to macroscopic solid behavior, one is most often confronted with
coupled PDE-ODE systems that behave very badly and for which classical PDE methods fail. A modicum of order can be restored with the introduction of
a notion of unilateral stability. However the resulting energetic framework still displays marginal or severe loss of convexity resulting in non-smoothness and/or
I will illustrate this conundrum on a simple 1d-example and proceed to analyze the impact of stability on the three archetypical irreversible solid behaviors, namely
plasticity, fracture and damage. This will take us from the (moderately) good to the (decidedly) bad, and finally to the (unabashedly) ugly.