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International Journal for Multiscale Computational Engineering

Impact factor: 1.103

ISSN Print: 1543-1649
ISSN Online: 1940-4352

International Journal for Multiscale Computational Engineering

DOI: 10.1615/IntJMultCompEng.v9.i3.30
pages 271-303

LARGE-SCALE COMPUTATIONS OF EFFECTIVE ELASTIC PROPERTIES OF RUBBER WITH CARBON BLACK FILLERS

Aurelie Jean
MINES ParisTech, Centre de Morphologie Mathématique, Mathématiques et Systémes; and Centre des Matériaux, CNRS UMR, France
Francois Willot
MINES-ParisTech, Centre de Morphologie Mathématique, Mathématiques et Systémes, France
S. Cantournet
MINES ParisTech, Centre des Matériaux, CNRS UMR, France
Samuel Forest
MINES MINES ParisTech, Centre des Matériaux, CNRS UMR, France
Dominique Jeulin
MINES-ParisTech, Centre de Morphologie Mathématique, Mathématiques et Systémes, France

ABSTRACT

A general method, based on a multiscale approach, is proposed to derive the effective elastic shear modulus of a rubber with 14% carbon black fillers from finite element and fast Fourier transform methods. The complex multiscale microstructure of such material was generated numerically from a mathematical model of its morphology that was identified from statistical moments out of transmission electron microscopy images. For finite element computations, the simulated microstructures were meshed from three-dimensional reconstruction of the isosurface using the marching cubes algorithm with special attention to the quality of the topology and the geometry of the mesh. To compute the shear modulus and to determine the representative volume element, homogeneous boundary conditions were prescribed on meshes and combined with a domain decomposition method. Regarding parallel computing, specific difficulties related to the highly heterogeneous microstructures and complex geometry are pointed out. The experimental shear modulus (1.8 MPa) obtained from dynamic mechanical analysis was estimated by the Hashin-Shtrikman lower bound ( 1.4 MPa) and the computations on simulated microstructures ( 2.4 MPa). The shear modulus was determined for two materials with the same volume fraction but different distribution of fillers. The current model of microstructures is capable of estimating the relative effect of the mixing time in processing associated with change in morphology on the elastic behavior. The computations also provide the local fields of stress/strain in the elastomeric matrix.