An analytical approach to modeling the stochastic behavior of visco-elastic materials

authored by: Philipp Junker, Jan Nagel
Abstract: Stochastic fluctuations of material properties, i.e. the elastic constants, result in stochastic fluctuations of the material's response to mechanical loading, i.e. the stresses. In this contribution, we present an analytical approach to the time-efficient and mathematically accurate modeling of the stochastic behavior of visco-elastic materials. The material behavior is modeled using a viscous strain as an internal variable whose evolution is described by a differential equation. Since the stochastic material properties enter the evolution equation, a stochastic differential equation has to be treated which renders the problem rather uncomfortable. However, we present a precise investigation of the problem that yields a treatment similar to the deterministic case but resulting in the analytical estimation both of the expectation value and the variance (and standard deviation) of the stresses. A numerical comparison to Monte Carlo simulations proves the reliability of our approach.
External Organisation(s): Ruhr-Universität Bochum
Eindhoven University of Technology (TU/e)
Type: Article
Journal: Zeitschrift für angewandte Mathematik und Mechanik
Volume: 98
Pages: 1249-1260
No. of pages: 12
Publication date: 04.07.2018
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Computational Mechanics, Applied Mathematics
Electronic version(s): https://doi.org/10.1002/zamm.201700257 (Access: Closed)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{38933aa3ce6e4097823453e56000bc64,
title = "An analytical approach to modeling the stochastic behavior of visco-elastic materials",
abstract = "Stochastic fluctuations of material properties, i.e. the elastic constants, result in stochastic fluctuations of the material's response to mechanical loading, i.e. the stresses. In this contribution, we present an analytical approach to the time-efficient and mathematically accurate modeling of the stochastic behavior of visco-elastic materials. The material behavior is modeled using a viscous strain as an internal variable whose evolution is described by a differential equation. Since the stochastic material properties enter the evolution equation, a stochastic differential equation has to be treated which renders the problem rather uncomfortable. However, we present a precise investigation of the problem that yields a treatment similar to the deterministic case but resulting in the analytical estimation both of the expectation value and the variance (and standard deviation) of the stresses. A numerical comparison to Monte Carlo simulations proves the reliability of our approach.",
keywords = "analytical solution, energy relaxation, stochastic material behavior, stress expectation and variance, visco-elastic material",
author = "Philipp Junker and Jan Nagel",
note = "{\textcopyright} 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim",
year = "2018",
month = jul,
day = "4",
doi = "10.1002/zamm.201700257",
language = "English",
volume = "98",
pages = "1249--1260",
journal = "Zeitschrift f{\"u}r angewandte Mathematik und Mechanik",
issn = "1521-4001",
publisher = "Wiley-VCH Verlag",
number = "7",
}