Morphology-based homogenization for viscoelastic particulate composites: Part I: Viscoelasticity sole

The complex problem of micromechanically based constitutive description of heterogeneous materials containing viscoelastic constituents is treated employing the method initially proposed by Christoffersen (1983) for elastic bonded granulates. It is built on a series of geometric and kinematic hypotheses concerning a granular assembly with interconnecting layers and offers an advantage of accounting – in a direct manner – for a microstructural morphology. context of viscoelastic behaviour considered, it is shown here that the Christoffersen-type homogenization preserves complex effects of internal viscoelastic interactions between viscoelastic matrix and elastic charge particles. The ‘long range memory effect’ (Suquet, 1987) consequent to the proper treatment of viscoelastic interactions is manifest through purely analytical, direct procedure. The latter involves a full set of internal relaxation variables relative to morphological discretization relative to a finite number of interconnecting layers in a representative volume. A complementary localization–homogenization procedure is thus proposed leading to a simplified model where a single global relaxation variable is substituted for the above full (discrete) set. The simplification procedure preserves an essential part of viscoelastic interactions of material constituents and the foregoing ‘long memory’ features. Furthermore it generates a legible viscoelastic model available for engineering applications. ompanion paper (Nadot-Martin, Trumel and Dragon, 2003, in preparation), the extension of the above scale transition in presence of damage by incorporating material discontinuities at grain/matrix interfaces tends to confirm the potentiality of the approach advanced.