Mechanics and Acoustics of Viscoelastic Composites by Micro-Macro Mean-Field Approach

We develop mean-field homogenization schemes for the prediction of the effective mechanical and acoustical properties of viscoelastic inclusion-reinforced materials. For mechanical applications, the overall behavior (e.g. stiffness tensor) of composite materials is estimated using Eshelby-based homogenization models. The effective acoustical properties (e.g. attenuation factor) are obtained in a similar way, based on the one particle scattering problem. Viscoelastic materials are known to be mechanical dampers characterised by their loss factor. The latter has also an impact on sound propagation through these materials. For elastic composites the scattering of waves on the inclusions is responsible for sound attenuation. For materials made of viscoelastic components both phenomena, material damping and particle scattering, must be taken into account. We present general Eshelby-based procedures able to predict the viscoelastic mechanical properties of multiphase — more than two — composites. There is the two-step homogenization procedure which besides the usual assumptions of Eshelby-based models, does not suffer any restriction in terms of material properties, aspect ratio or orientation. We also propose a two-level recursive scheme for matrix materials with coated inclusions. We implemented the Mori-Tanaka (M-T) model and a non-trivial interpolation between M-T and inverse M-T estimates to achieve the stages of those procedures.We made (see [1]) extensive confrontations with experimental data or unit cell finite element (FE) simulations. For a large variety of viscoelastic composite materials, the proposed schemes perform much better than other existing homogenization methods. We propose homogenization schemes to predict the effective acoustical properties of viscoelastic composites. It is an extension of the effective medium approach for wave propagation in inclusion-reinforced materials widely studied by various authors (e.g. [2] and references therein) in the framework of linear elasticity. In their approach, every inclusion behaves as isolated in a medium with the effective properties of the composite. We wish to avoid the self-consistent nature of the formulation and study adaptations of the M-T and interpolative models to the scattering problem.