Modeling of viscoelastic structures with random material properties using time‐separated stochastic mechanics

authored by: Philipp Junker, Jan Nagel
Abstract: Modeling and simulation of materials with stochastic properties is an emerging field in both mathematics and mechanics. The most important goal is to compute the stochastic characteristics of the random stress, such as the expectation value and the standard deviation. An accurate approach are Monte Carlo simulations; however, they consume drastic computational power due to the large number of stochastic realizations that have to be simulated before convergence is achieved. In this paper, we show that a recently published approach for accurate modeling of viscoelastic materials with stochastic material properties at the material point level in the work of Junker and Nagel is also valid for macroscopic bodies. The method is based on a separation of random but time-invariant variables and time-dependent but deterministic variables for the strain response at the material point (time-separated stochastic mechanics [TSM]). We recall the governing equations, derive a simplified form, and discuss the numerical implementation into a finite element routine. To validate our approach, we compare the TSM simulations with Monte Carlo simulations, which provide the “true” answer but at unaffordable computational costs. In contrast, the numerical effort of our approach is in the same range as for deterministic viscoelastic simulations.
External Organisation(s): The University of Wuppertal
Type: Article
Journal: International Journal for Numerical Methods in Engineering
Volume: 121
Pages: 308-333
No. of pages: 26
ISSN: 0029-5981
Publication date: 09.12.2019
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Numerical Analysis, Engineering(all), Applied Mathematics
Electronic version(s): https://doi.org/10.1002/nme.6210 (Access: Open)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{640f40625d8944cfb9f6910dbb855bd1,
title = "Modeling of viscoelastic structures with random material properties using time‐separated stochastic mechanics",
abstract = "Modeling and simulation of materials with stochastic properties is an emerging field in both mathematics and mechanics. The most important goal is to compute the stochastic characteristics of the random stress, such as the expectation value and the standard deviation. An accurate approach are Monte Carlo simulations; however, they consume drastic computational power due to the large number of stochastic realizations that have to be simulated before convergence is achieved. In this paper, we show that a recently published approach for accurate modeling of viscoelastic materials with stochastic material properties at the material point level in the work of Junker and Nagel is also valid for macroscopic bodies. The method is based on a separation of random but time-invariant variables and time-dependent but deterministic variables for the strain response at the material point (time-separated stochastic mechanics [TSM]). We recall the governing equations, derive a simplified form, and discuss the numerical implementation into a finite element routine. To validate our approach, we compare the TSM simulations with Monte Carlo simulations, which provide the “true” answer but at unaffordable computational costs. In contrast, the numerical effort of our approach is in the same range as for deterministic viscoelastic simulations.",
keywords = "Monte Carlo simulations, finite element method, stochastic material behavior, stress expectation and variance, viscoelastic material",
author = "Philipp Junker and Jan Nagel",
note = "Publisher Copyright: {\textcopyright} 2019 The Authors. International Journal for Numerical Methods in Engineering Published by John Wiley & Sons, Ltd. Copyright: Copyright 2019 Elsevier B.V., All rights reserved.",
year = "2019",
month = dec,
day = "9",
doi = "10.1002/nme.6210",
language = "English",
volume = "121",
pages = "308--333",
journal = "International Journal for Numerical Methods in Engineering",
issn = "0029-5981",
publisher = "John Wiley and Sons Ltd",
number = "2",
}