Abstract

This paper presents stability results for rate-independent mechanical systems, associated with general tangent stiffness matrices including symmetric and nonsymmetric ones. Conservative and nonconservative as well as associate and nonassociate elastoplastic systems are concerned by such a theoretical study. Hill’s stability criterion, also called the second-order work criterion, is here revisited in terms of kinematically constrained systems. For piecewise rate-independent mechanical systems (which may cover inelastic and elastic evolution processes), such a criterion is also a divergence Lyapunov stability criterion for any kinematic autonomous constraints. This result is here extended for systems with nonsymmetric tangent matrices. By virtue of a new type of variational formulation on the possible kinematic constraints, and thanks to the concept of kinematical structural stability (KISS), both criteria, Hill’s stability criterion and the divergence stability criterion under kinematic constraints, are shown to be equivalent.

Keywords

Physics and Astronomy Classification Scheme 2010

Mathematical Subject Classification 2010

Milestones

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