Weak solvability via bipotentials for contact problems with power-law friction

Matei, Andaluzia; Osiceanu, Madalina

doi:10.1016/j.jmaa.2023.127064

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2024

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“…In connection with the calculus of variations, the bipotential theory allowed to deliver two-field variational formulations for many boundary value problems. Such formulations were proposed for several models in contact mechanics, see [9,16,17,18,19,20,21,22], where the existence and uniqueness of the pair solutions consisting of the displacement vector and the Cauchy stress tensor have been studied.…”

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confidence: 99%

A Variational Formulation Governed by Two Bipotentials for a Frictionless Contact Model

Matei,

Osiceanu

2024

Mathematical Modelling and Analysis

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We consider a frictionless contact model whose constitutive law and contact condition are described by means of subdifferential inclusions. For this model, we deliver a variational formulation based on two bipotentials. Our formulation envisages the computation of a three-field unknown consisting of the displacement vector, the stress tensor and the normal stress on the contact zone, the contact being described by a generalized Winkler condition. Subsequently, we obtain existence and uniqueness results. Some properties of the solution are also discussed, focusing on the data dependence.

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