Abstract
In this paper, a concept of stability of quasi-static paths is discussed. This takes into account the existence of fast (dynamic) and slow (quasi-static) times scales in the mechanical systems that have an elastic-plastic behavior with linear hardening. The proposed concept is essentially a continuity property relative to the size of the initial perturbations (as in Lyapunov stability) and relative to the smallness of the rate of application of the forces (which here plays the role of the small parameter in singular perturbation problems). Existence and uniqueness results for the dynamic and quasi-static problems are recalled and the stability of quasi-static paths for elastic-plastic systems with hardening is obtained.
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