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High-dimension polynomial chaos expansions of effective constitutive equations for hyperelastic heterogeneous random microstructures

Abstract : In this research, we address the construction of random effective constitutive equations by nonlinear stochastic homogenization of hyperelastic heterogeneous materials for which a high number of random parameters is needed to characterize the uncertainties at the microscopic scale. We base our new approach on a non-concurrent multiscale method recently proposed for computing the homogenization of nonlinear heterogeneous materials which still represents a difficult task. This technique, based on a numerical construction of the strain energy density function associated with a microstructure, allows this difficulty to be encountered in a deterministic framework. However, in order to obtain an efficient mechanical model, one must take into account the different sources of uncertainties related to the material at the microscopic level.
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Contributor : Christian Soize <>
Submitted on : Thursday, September 20, 2012 - 9:16:56 PM
Last modification on : Thursday, March 19, 2020 - 11:52:03 AM
Long-term archiving on: : Friday, December 21, 2012 - 3:52:10 AM

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  • HAL Id : hal-00734170, version 1

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A. Clément, Christian Soize, Julien Yvonnet. High-dimension polynomial chaos expansions of effective constitutive equations for hyperelastic heterogeneous random microstructures. Congress on Computational Methods in Applied Sciences and Engineering (ECCOMAS 2012), Vienna University of Technology, Sep 2012, Vienna, Austria. pp.1-2. ⟨hal-00734170⟩

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