Application of the incremental variational approach (EIV model) to the linear viscoelastic homogenization of different types of microstructures: long fiber-, particle-reinforced and strand-based composites

This paper focusses on the incremental variational approach proposed by Lahellec, N., and Suquet, P., Int. J. Solids Struct. 44, 507-529, 2007, commonly called EIV approach in the literature, and applied to linear viscoelastic heterogeneous media. The objective is to progress in the evaluation of this specific approach by complementary investigations in configurations (microstructure and loading) already envisioned by the previous authors, and also in new configurations involving other microstructures and/or linear schemes. This is accomplished through comparisons with reference solutions obtained by the Laplace transform (LT) or full-field finite element (FE) simulations, or with other existing mean-field approaches. At first, the ability of the EIV model to deal with the effective response of long fiber composites with periodic microstructure, evidenced by Lahellec and Suquet with the Hashin-Shritkman approximation, is here retrieved with an alternative linear scheme. Supplementary analysis involving different contrasts and matrix viscosities or regarding the quality of the phase averages highlight the reliability of the approach. Then, results obtained for spherical particle-reinforced composites illustrate the capability of the EIV model, coupled to the Mori-Tanaka (MT) and Double-Inclusion (DI) schemes, to estimate the effective responses with a precision in accordance with the known performances of both linear schemes. In addition, the overall response to a tensile loading estimated by the coupled (EIV + MT) is shown to be more accurate than the additive tangent Mori-Tanaka estimate. A last application concerns strand-based wood composites for which the global anisotropy is induced by both the morphology and the orthotropic nature of the elastic phase. The EIV approach is associated with a specific linear scheme to this end. The first estimates obtained under relaxation loadings (uniaxial and shear) are encouraging when compared to FE reference solutions.