A dynamic viscoelastic problem with friction and rate-depending contact interactions

Marius Cocou (1)

1 LMA - Laboratoire de Mécanique et d'Acoustique [Marseille]

The aim of this work is to study a dynamic problem that constitutes a unified approach to describe some rate-depending interactions between the boundaries of two viscoelastic bodies, including relaxed unilateral contact, pointwise friction or adhesion conditions. The classical formulation of the problem is presented and two variational formulations are given as three and four-field evolution implicit equations. Based on some approximation results and an equivalent fixed point problem for a multivalued function, we prove the existence of solutions to these variational evolution problems.

Mots clés: Dynamic problems; contact interactions; Coulomb friction; viscoelasticity; set-valued mapping.

Domaines: Mécanique des solides [physics.class-ph]

Marius Cocou. A dynamic viscoelastic problem with friction and rate-depending contact interactions. Evolution Equations and Control Theory, 2020, 9 (4), pp.981-993. ⟨10.3934/eect.2020060⟩. ⟨hal-02999322⟩