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Second-order work criterion and divergence criterion: a full equivalence for kinematically constrained systems

Abstract : This paper presents stability results for rate-independent mechanical systems, associated with general tangent stiffness matrices including symmetric and non-symmetric 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 non-symmetric 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.
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https://hal.inrae.fr/hal-03254348
Contributor : Christopher Lallemant <>
Submitted on : Monday, June 14, 2021 - 5:48:16 PM
Last modification on : Monday, June 14, 2021 - 6:01:07 PM

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Jean Lerbet, Noël Challamel, François Nicot, Felix Darve. Second-order work criterion and divergence criterion: a full equivalence for kinematically constrained systems. Mathematics and Mechanics of Complex Systems, International Research Center for Mathematics & Mechanics of Complex Systems (M&MoCS),University of L’Aquila in Italy, 2020, 8 (1), pp.1-28. ⟨10.2140/memocs.2020.8.1⟩. ⟨hal-03254348⟩

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