Assessing the “(in)stability of quasi-static paths”

In this paper, a concept of “stability of quasi-static paths” that takes into account the existence of fast (dynamic) and slow (quasi-static) time scales is discussed. It is essentially a continuity property with respect to the smallness of the initial perturbations (as in Liapunov stability) and to the smallness of the quasi-static loading rate (that plays the role of the small parameter in singular perturbation problems). Three mechanical examples are presented that illustrate the similarities, the differences and the relations between this concept of “stability of quasi-static paths” and the one of Liapunov stability of some related equilibrium configurations or dynamic trajectories.