Exact asymptotic relations for the effective response of linear viscoelastic heterogeneous media

Valentin Gallican (1) , Renald Brenner (2) , Pierre Suquet (3)

1 DALEMBERT - Institut Jean Le Rond d'Alembert
2 IJLRDA-MISES - Mécanique et Ingénierie des Solides Et des Structures
3 LMA - Laboratoire de Mécanique et d'Acoustique [Marseille]

This article addresses the asymptotic response of viscoelastic heterogeneous media in the frequency domain, at high and low frequencies, for different types of elementary linear viscoelastic constituents. By resorting to stationary principles for complex viscoelasticity and adopting a classification of the viscoelastic behaviours based on the nature of their asymptotic regimes, either elastic or viscous, four exact relations are obtained on the overall viscoelastic complex moduli in each case. Two relations are related to the asymptotic uncoupled heterogeneous problems while the two remaining ones result from the viscoelastic coupling which manifests itself in the transient regime. These results also provide exact conditions on certain integrals in time of the effective relaxation spectrum. This general setting encompasses the results obtained in preceding studies on mixtures of Maxwell constituents.

Mots clés: viscoelasticity; composite; homogenization

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

Valentin Gallican, Renald Brenner, Pierre Suquet. Exact asymptotic relations for the effective response of linear viscoelastic heterogeneous media. Comptes Rendus Mécanique, 2017, 345 (11), pp.742-751. ⟨10.1016/j.crme.2017.09.001⟩. ⟨hal-01582070⟩