Four exact relations for the effective relaxation function of linear viscoelastic composites

Pierre Suquet (1)

1 M&S - Matériaux et Structures

This study is devoted to viscoelastic composites composed from individual Maxwell constituents. The effective constitutive relations of such composites exhibit a long memory effect which manifests itself through an integral kernel (the effective relaxation function of the composite). Four asymptotic relations for this integral kernel are derived which require only the resolution of linear elastic (or purely viscous) problems. These four relations can be used in an approximate model with two relaxation times (for incompressible, isotropic composites). The model is exact for specific microstructures but is an approximation in general. Its accuracy is discussed by comparison with full-field simulations.

Mots clés: Viscoelasticity; Composites

Domaines: Matériaux et structures en mécanique [physics.class-ph]; Matériaux et structures en mécanique [physics.class-ph]

Pierre Suquet. Four exact relations for the effective relaxation function of linear viscoelastic composites. Comptes Rendus Mécanique, 2012, 340 (4-5), pp.387-399. ⟨10.1016/j.crme.2012.02.022⟩. ⟨hal-00683860⟩