Towards a non-linear micromechanics-based analysis for particulate composites

A non-classical multiscale modelling for viscoelastic particulate composites has been proposed by Nadot-Martin et al. [Nadot-Martin C, Trumel H, Dragon A. Morphology-based homogenization for viscoelastic particulate composites: Part I: Viscoelasticity sole. Eur. J. Mech. A/Solids 2003;22:89–106]. It is based on the geometrical and kinematical framework advanced first by Christoffersen [Christoffersen J. Bonded granulates. J. Mech. Phys. Solids 1983;31:55–83] in the context of linear elastic constituents and presents an interesting alternative with respect to more widely employed self-consistent like methods. Its specific feature consists in accounting for a specific multiple-grains-and-matrix-layers related microstructural morphology characterizing highly filled composites. Salient textural features of the aggregate can be preserved via homogenization put forward. The viscoelastic homogenization, performed in [Nadot-Martin C, Trumel H, Dragon A. Morphology-based homogenization for viscoelastic particulate composites: Part I: Viscoelasticity sole. Eur. J. Mech. A/Solids 2003;22:89–106], was realized in the small strain context. The present study aims at extending the methodology into the finite deformation range thus making it applicable for a class of assemblies containing highly deformable elastomeric matrix. As the first stage of geometrically non-linear scale transition, the non-hereditary, hyperelastic behaviour of constituents is considered. After specific formal developments, numerical solutions for particular (regular) microstructure and loading paths show the feasibility of the procedure and its advantages, notably accessibility of estimated local fields.