Hydrodynamic reinforcement in filled polymer systems: numerical simulations and non-linear modeling

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The aim of the present project is to develop an analytical stress and strain amplification approach (SSAA) for the description of the non-linear mechanical response in polymer melts and networks containing spherical and anisometric rigid inclusions up to moderate filler loadings. The SSAA is valid in a continuum limit, when the (smallest) size of particles exceeds the average end-to-end distance of polymer chains or strands. An important feature of the SSAA is that it accounts for pure hydrodynamic reinforcement by non-aggregating filler particles which do not interact attractively or repulsively with surrounding polymer chains and each other. Hence, the SSAA should enable in future a clear separation between the effect of hydrodynamic reinforcement and other reinforcement effects arising for example due to the presence of filler agglomerates / network or due to the chain localization on the filler surface.In the case of filled polymer melts, the SSAA which has already been applied to the Bird-Carreau model in the dilute limit, will be further developed for higher volume fractions of particles and different particle aspect ratios. It is planned to consider stationary shear and elongational flows. In the case of filled elastomers, the SSAA will be developed for a number of non-linear constitutive models with increasing complexity such as the Neo-Hooke model, the Mooney-Rivlin model and the extended tube-model for rubber elasticity. The separation of the hydrodynamic amplification factor into the stress and strain amplification factors will be done by direct comparison between predictions of an analytically modified constitutive equation with results from numerical homogenisation.