Mechanics and acoustics of viscoelastic inclusion reinforced composites : micro-macro modeling of effective properties/

We develop homogenization schemes for the effective mechanical and acoustical properties of linear viscoelastic inclusion reinforced composites. Generic procedures are studied and proposed, starting from the statics and elastic materials, followed by viscoelastic behaviors and the quasi-static approximation, to end up with dynamic viscoelastic models. For elastic composites, our main contributions regard homogenization schemes for coated inclusion reinforced materials. An original two-level recursive procedure is proposed. At each level, a homogenization model suitable for two-phase composites with aligned reinforcements is required. That makes the procedure very generic. The latter is used as stand-alone (i.e. for three-phase composites) or to achieve the first step of a two-step approach for multiphase materials (e.g. composites with misaligned coated fibers). With the quasi-static approximation, i.e. when inertial effects are ignored, we generalize the generic two-step and two-level procedures to predict both time dependent and harmonic effective mechanical properties (storage and loss moduli) of linear viscoelastic multiphase composites. The static and quasi-static models however cannot account for attenuation of acoustic waves due to scattering by the inclusions. Effective acoustic properties (phase velocities, attenuation factors) of viscoelastic inclusion reinforced composites are addressed by dynamic schemes. We propose a generic framework for the development of such homogenization models. It generalizes and unifies within a single formulation several methods of the literature. An independent-scattering model is derived. The link between dynamic schemes in the long-wave region and static models is shown. Finally, these homogenization schemes are integrated in a finite element model based on a discontinuous Galerkin formulation of the Helmholtz equation to simulate acoustic problems involving viscoelastic composite materials.