Dynamics of elastic bodies connected by a thin soft viscoelastic layer

Christian Licht (1) , Alain Léger (2) , Somsak Orankitjaroen (3) , Ahmed Ould Khaoua (4)

1 M3 - Modélisation Mathématique en Mécanique
2 M&S - Matériaux et Structures
3 Department of Mathematics
4 Département de Mathématiques

A dynamic study was performed on a structure consisting of two three-dimensional linearly elastic bodies connected by a thin soft nonlinear Kelvin-Voigt viscoelastic adhesive layer. The adhesive is assumed to be viscoelastic of Kelvin-Voigt generalized type, which makes it possible to deal with a relatively wide range of physical behavior by choosing suitable dissipation potentials. In the static and purely elastic case, convergence results when geometrical and mechanical parameters tend to zero have already been obtained using variational convergence methods. To obtain convergence results in the dynamic case, the main tool, as in the quasistatic case, is a nonlinear version of Trotter's theory of approximation of semigroups acting on variable Hilbert spaces. The limit problem involves a mechanical constraint imposed along the surface to which the layer shrinks. The meaning of this limit with respect to the relative behavior of the parameters is discussed. The problem applies in particular to wave phenomena in bonded domains.

Mots clés: Approximation of semigroups; Bonding problem; Kelvin-Voigt viscoelasticity; Trotter's theory; Variational convergence; Wave propagation

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

Christian Licht, Alain Léger, Somsak Orankitjaroen, Ahmed Ould Khaoua. Dynamics of elastic bodies connected by a thin soft viscoelastic layer. Journal de Mathématiques Pures et Appliquées, 2013, 99 (6), pp.685-703. ⟨10.1016/j.matpur.2012.10.005⟩. ⟨hal-00799595⟩