Modeling the behavior of elastic materials with stochastic microstructure

authored by: J. Nagel, P. Junker
Abstract: Even in the simple linear elastic range, the material behavior is not deterministic, but fluctuates randomly around some expectation values. The knowledge about this characteristic is obviously trivial from an experimentalist’s point of view. However, it is not considered in the vast majority of material models in which “only” deterministic behavior is taken into account. One very promising approach to the inclusion of stochastic effects in modeling of materials is provided by the Karhunen-Loève expansion. It has been used, for example, in the stochastic finite element method, where it yields results of the desired kind, but unfortunately at drastically increased numerical costs. This contribution aims to propose a new ansatz that is based on a stochastic series expansion, but at the Gauß point level. Appropriate energy relaxation allows to derive the distribution of a synthesized stress measure, together with explicit formulas for the expectation and variance. The total procedure only needs negligibly more computation effort than a simple elastic calculation. We also present an outlook on how the original approach in [7] can be applied to inelastic materials.
Organisation(s): Institute of Continuum Mechanics
External Organisation(s): Eindhoven University of Technology (TU/e)
Ruhr-Universität Bochum
Type: Conference contribution
Pages: 296-307
No. of pages: 12
Publication date: 2017
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Computational Theory and Mathematics, Theoretical Computer Science
: Details in the research portal "Research@Leibniz University"

BibTeX

@inproceedings{b36ec0e4ffaf454d98c7c9d6645506f7,
title = "Modeling the behavior of elastic materials with stochastic microstructure",
abstract = "Even in the simple linear elastic range, the material behavior is not deterministic, but fluctuates randomly around some expectation values. The knowledge about this characteristic is obviously trivial from an experimentalist{\textquoteright}s point of view. However, it is not considered in the vast majority of material models in which “only” deterministic behavior is taken into account. One very promising approach to the inclusion of stochastic effects in modeling of materials is provided by the Karhunen-Lo{\`e}ve expansion. It has been used, for example, in the stochastic finite element method, where it yields results of the desired kind, but unfortunately at drastically increased numerical costs. This contribution aims to propose a new ansatz that is based on a stochastic series expansion, but at the Gau{\ss} point level. Appropriate energy relaxation allows to derive the distribution of a synthesized stress measure, together with explicit formulas for the expectation and variance. The total procedure only needs negligibly more computation effort than a simple elastic calculation. We also present an outlook on how the original approach in [7] can be applied to inelastic materials.",
keywords = "Analytical solution, Energy relaxation, Stochastic material behavior, Stochastic series expansion, Stress expectation, Variance",
author = "J. Nagel and P. Junker",
note = "Publisher Copyright: {\textcopyright} 2017 International Center for Numerical Methods in Engineering. All rights reserved. Copyright: Copyright 2018 Elsevier B.V., All rights reserved.; 14th International Conference on Computational Plasticity - Fundamentals and Applications, COMPLAS 2017 ; Conference date: 05-09-2017 Through 07-09-2017",
year = "2017",
language = "English",
series = "Proceedings of the 14th International Conference on Computational Plasticity - Fundamentals and Applications, COMPLAS 2017",
publisher = "International Center for Numerical Methods in Engineering",
pages = "296--307",
editor = "Eugenio Onate and Djordje Peric and Owen, {D. Roger J.} and Michele Chiumenti",
booktitle = "Proceedings of the 14th International Conference on Computational Plasticity - Fundamentals and Applications, COMPLAS 2017",
}