Modified SFEM for computational homogenization of heterogeneous materials with microstructural geometric uncertainties

Pivovarov, D. and Steinmann, P. (2016) Modified SFEM for computational homogenization of heterogeneous materials with microstructural geometric uncertainties. Computational Mechanics, 57(1), pp. 123-147. (doi: 10.1007/s00466-015-1224-4)

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Abstract

In the current work we examine the application of the stochastic finite element method (SFEM) to the modeling of representative volume elements for heterogeneous materials. Uncertainties in the geometry of the microstructure result in the random nature of the solution fields thus requiring use of the stochastic version of the finite element method. For considering large differences in the material properties of matrix and inclusions a standard SFEM approach proves not stable and results in high numerical errors compared to a brute-force Monte-Carlo evaluation. Therefore in order to stabilize the SFEM we propose an alternative Gauss integration rule as resulting from a truncation of the probability density function for the random variable. In addition we propose new basis functions substituting the common polynomial chaos expansion, resulting in higher accuracy for the standard deviation in the homogenized stress at the macro scale.

Item Type:Articles
Additional Information:The support of this work by the ERC Advanced Grant MOCOPOLY and Deutsche Forschungs-Gemeinschaft (DFG) through the Cluster of Excellence Engineering of Advanced Materials is gratefully acknowledged.
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Steinmann, Professor Paul
Authors: Pivovarov, D., and Steinmann, P.
College/School:College of Science and Engineering > School of Engineering > Infrastructure and Environment
Journal Name:Computational Mechanics
Publisher:Springer
ISSN:0178-7675
ISSN (Online):1432-0924
Published Online:28 November 2015

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