Dynamics of Two Linearly Elastic Bodies Connected by a Heavy Thin Soft Viscoelastic Layer

Elena Bonetti (1) , Giovanna Bonfanti (2) , Christian Licht (3, 4) , Riccarda Rossi (2)

1 UNIMI - Università degli Studi di Milano = University of Milan
2 UniBs - Università degli Studi di Brescia = University of Brescia
3 MéTICE - Mécanique Théorique, Interface, Changements d’Echelles
4 Mahidol University [Bangkok]

In this paper we extend the asymptotic analysis in [18], performed on a structure consisting of two linearly elastic bodies connected by a thin soft nonlinear KelvinVoigt viscoelastic adhesive layer, to the case in which the total mass of the layer remains strictly positive as its thickness tends to zero. We obtain convergence results by means of a nonlinear version of Trotter's theory of approximation of semigroups acting on variable Hilbert spaces. Differently from the limit models derived in [18], in the present analysis the dynamic effects on the surface on which the layer shrinks do not disappear. Thus, the limiting behavior of the remaining bodies is described not only in terms of their displacements on the contact surface, but also by an additional variable that keeps track of the dynamics in the adhesive layer.

Domaines: Sciences de l'ingénieur [physics]

Elena Bonetti, Giovanna Bonfanti, Christian Licht, Riccarda Rossi. Dynamics of Two Linearly Elastic Bodies Connected by a Heavy Thin Soft Viscoelastic Layer. Journal of Elasticity, 2020, 141 (1), pp.75-107. ⟨10.1007/s10659-020-09776-7⟩. ⟨hal-03346719⟩