Fuzzy-stochastic FEM-based homogenization framework for materials with polymorphic uncertainties in the microstructure

Pivovarov, D., Oberleiter, T., Willner, K. and Steinmann, P. (2019) Fuzzy-stochastic FEM-based homogenization framework for materials with polymorphic uncertainties in the microstructure. International Journal for Numerical Methods in Engineering, 116(9), pp. 633-660. (doi: 10.1002/nme.5947)

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Abstract

Uncertainties in the macroscopic response of heterogeneous materials result from two sources: the natural variability in the microstructure's geometry and the lack of sufficient knowledge regarding the microstructure. The first type of uncertainty is denoted aleatoric uncertainty and may be characterized by a known probability density function. The second type of uncertainty is denoted epistemic uncertainty. This kind of uncertainty cannot be described using probabilistic methods. Models considering both sources of uncertainties are called polymorphic. In the case of polymorphic uncertainties, some combination of stochastic methods and fuzzy arithmetic should be used. Thus, in the current work, we examine a fuzzy‐stochastic finite element method–based homogenization framework for materials with random inclusion sizes. We analyze an experimental radii distribution of inclusions and develop a stochastic representative volume element. The stochastic finite element method is used to obtain the material response in the case of random inclusion radii. Due to unavoidable noise in experimental data, an insufficient number of samples, and limited accuracy of the fitting procedure, the radii distribution density cannot be obtained exactly; thus, it is described in terms of fuzzy location and scale parameters. The influence of fuzzy input on the homogenized stress measures is analyzed.

Item Type:Articles
Additional Information:European Research Council, Grant/Award Number: MOCOPOLY; DeutscheForschungs-Gemeinschaft (DFG),Grant/Award Number: Priority Program SPP1886 and DFG FOR 2271
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Steinmann, Professor Paul
Authors: Pivovarov, D., Oberleiter, T., Willner, K., and Steinmann, P.
College/School:College of Science and Engineering > School of Engineering > Infrastructure and Environment
Journal Name:International Journal for Numerical Methods in Engineering
Publisher:Wiley
ISSN:0029-5981
ISSN (Online):1097-0207
Published Online:31 August 2018
Copyright Holders:Copyright © 2018 John Wiley and Sons Ltd
First Published:First published in International Journal for Numerical Methods in Engineering 116(9):633-660
Publisher Policy:Reproduced in accordance with the copyright policy of the publisher

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