Open Access

ARTICLE

Parameter Sensitivity and Probabilistic Analysis of the Elastic Homogenized Properties for Rubber Filled Polymers

by Marcin Kami ´nski¹, Bernd Lauke²

1 Department of Structural Mechanics, Faculty of Civil Engineering, Architecture and Environmental Engineering, Technical University of Lódź, Al. Politechniki 6, 90-924 Lódź, Poland.
  Tel: 48-42-6313571 Email: Marcin.Kaminski@p.lodz.pl
2 Leibniz-Institut für Polymerforschung Dresden e.V., Hohe Strasse 6, 01069 Dresden, Germany.
  Email: laukeb@ipfdd.de

Computer Modeling in Engineering & Sciences 2013, 93(6), 411-440. https://doi.org/10.3970/cmes.2013.093.411

Abstract

The main aim in this paper is a computational study devoted to the sensitivity gradients and probabilistic moments of the effective elastic parameters for the rubber-filled polymers. The methodology is based on least squares recovery of the polynomial functions relating the effective tensor components and the given input design/random parameters. All numerical experiments are provided with respect to Young’s moduli of the elastomer constituents. Computational analysis is possible thanks to the application of the Response Function Method, which is enriched in our approach with the weighting procedures implemented according to the Dirac-type distributions. The homogenized elasticity tensor components are derived with the use of the variational upper and lower bounds for 2 D idealization of the composite and also thanks to the computational solution to the plane strain cell problem solved on the elastomer’s Representative Volume Element. Sensitivity analysis results in the first order gradients of the effective tensor, while probabilistic moments consist of up to the fourth order probabilistic moments and coefficients of the tensor; all numerical experiments are carried out in the FEM-oriented code MCCEFF and also using the symbolic computer algebra system MAPLE. This approach is straightforwardly applicable in deterministic and probabilistic optimization of polymers filled with rubber or carbon particles; it gives also the basis to further homogenization-based experiments with more advanced constitutive laws like Mullins theory.

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