Name
Title | ||
|---|---|---|
Multiscale Modeling of Viscoelastic Materials Containing Rigid Nonrotating Inclusions |
Abstract | ||
|---|---|---|
We introduce and apply a multiscale simulation method for the investigation of sheared viscoelastic materials containing rigid nonrotating 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, Kroger, and Hess [J. Non-Newtonian Fluid Mech., 105 ( 2002), pp. 35 - 51] 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 versus the volume fraction rho(v) of the inclusions. Up to small values of rho(v), excellent agreement with theoretical results for nonrotating inclusions is obtained. The effective shear viscosity increases linearly with rho(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; see Einstein [ Ann. d. Physik, 19 ( 1906), pp. 289 - 306], 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 nonlinear 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 numbers considered. The results indicate that the macroscopic rheology of the composite is determined by the constitutive equation governing the matrix only but characterized by rho(v)-dependent effective material functions. Finally, a detailed analysis of the hydrodynamic field within the viscoelastic matrix is presented. |
Year | DOI | Venue |
|---|---|---|
2006 | 10.1137/060651367 | MULTISCALE MODELING & SIMULATION |
Keywords | Field | DocType |
smoothed particle dynamics,viscoelasticity,composite materials,rigid inclusions,smoothed particle hydrodynamics,smooth particle applied mechanics,smoothed particle dissipative dynamics | Smoothed-particle hydrodynamics,Shear (sheet metal),Viscoelasticity,Mathematical analysis,Multiscale modeling,Viscosity,Mechanics,Newtonian fluid,Cauchy stress tensor,Constitutive equation,Physics | Journal |
Volume | Issue | ISSN |
5 | 3 | 1540-3459 |
Citations | PageRank | References |
0 | 0.34 | 1 |
Authors | ||
3 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Marco Ellero | 1 | 21 | 5.89 |
| Martin Kröger | 2 | 1 | 0.96 |
| Siegfried Hess | 3 | 1 | 0.96 |