| We introduce and apply a simulation method for the investigation of sheared viscoelastic materials containing rigid non-rotating cylindrical inclusions. The method is based on a classical Smoothed Particle Hydrodynamics (SPH) algorithm, modified for viscoelastic flows. The modified SPH incorporates a constitutive equation for the stress tensor (actually based on the corotational Jaumann-Maxwell model). This algorithm had been tested by Ellero et al. [J. Non-Newtonian Fluid Mech. 105, 35 (2002)] for transient flows in a channel geometry. In the present article, a bulk composite material subjected to steady shear is simulated in the case of a Newtonian solvent. For this example, we observe the expected linear increase of the macroscopic effective viscosity vs. the volume fraction ρ_v of the inclusions. Up to small values of ρ_v, excellent agreement with theoretical results for non-rotating inclusions is obtained. The effective shear viscosity increases linearly with ρ_v with a proportionality factor of about 3. This result differs from the two dimensional Einstein-like relation for a dilute suspension of freely-rotating cylinders, [Ann. d. Physik. 19, 289 (1906)], where a factor 2 is prescribed, and it is associated to the effect of an external applied torque. For larger values of the volume ratio, also the expected non-linear increase is observed indicating that interactions between inclusions become relevant. As a second example, a suspension of inclusions in a viscoelastic matrix is simulated showing an effective increase of the viscometric functions over all the range of Deborah number considered. The results indicate that the macroscopic rheology of the composite is determined by the constitutive equation governing the matrix only, but characterised by ρ_v-dependent effective material functions. Finally, a detailed analysis of the hydrodynamics field within the viscoelastic matrix is presented.
for LaTeX users @article{MEllero2006-5,
author = {M. Ellero and M. Kr\"oger and S. Hess},
title = {Multiscale modeling of viscoelastic materials containing rigid nonrotating inclusions},
journal = {Multiscale Model. Simul.},
volume = {5},
pages = {759-785},
year = {2006}
}
\bibitem{MEllero2006-5} M. Ellero, M. Kr\"oger, S. Hess,
Multiscale modeling of viscoelastic materials containing rigid nonrotating inclusions,
Multiscale Model. Simul. {\bf 5} (2006) 759-785.MEllero2006-5
M. Ellero, M. Kr\"oger, S. Hess
Multiscale modeling of viscoelastic materials containing rigid nonrotating inclusions
Multiscale Model. Simul.,5,2006,759-785 |
mk@mat.ethz.ch
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