Uncertainty quantification for viscoelastic composite materials using time-separated stochastic mechanics

authored by: Hendrik Geisler, Philipp Junker
Abstract: With the growing use of composite materials, the need for high-fidelity simulation techniques of the related behavior increases. One important aspect to take into account is the uncertainty of the response due to fluctuations of the material parameters of the constituent materials of the homogenized composite. This inherent randomness leads to stochastic stresses on the microscale and uncertain macroscale response. Until now, the viscoelastic response of the matrix material seriously hindered the application of efficient methods to predict the composite material behavior. In this work, a novel method based on the time-separated stochastic mechanics (TSM) is developed to address this problem. We present how the uncertainty of the microscale stresses of a representative volume element and the homogenized macroscale stresses can be approximated with a low number of deterministic finite element simulations. Quantities of interest are the expectation, standard deviation, and the probability distribution function of the stresses on micro- and macroscale. The results showcase that the TSM is able to approximate the reference results very well at a minimal fraction of the computational cost needed for Monte Carlo simulations.
Organisation(s): Institute of Continuum Mechanics
International RTG 2657: Computational Mechanics Techniques in High Dimensions
External Organisation(s): École normale supérieure Paris-Saclay (ENS Paris-Saclay)
Type: Article
Journal: Probabilistic Engineering Mechanics
Volume: 76
No. of pages: 11
ISSN: 0266-8920
Publication date: 04.2024
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Statistical and Nonlinear Physics, Civil and Structural Engineering, Nuclear Energy and Engineering, Condensed Matter Physics, Aerospace Engineering, Ocean Engineering, Mechanical Engineering
Electronic version(s): https://doi.org/10.1016/j.probengmech.2024.103618 (Access: Open)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{dd9fe51e29264de586654bc73e941b33,
title = "Uncertainty quantification for viscoelastic composite materials using time-separated stochastic mechanics",
abstract = "With the growing use of composite materials, the need for high-fidelity simulation techniques of the related behavior increases. One important aspect to take into account is the uncertainty of the response due to fluctuations of the material parameters of the constituent materials of the homogenized composite. This inherent randomness leads to stochastic stresses on the microscale and uncertain macroscale response. Until now, the viscoelastic response of the matrix material seriously hindered the application of efficient methods to predict the composite material behavior. In this work, a novel method based on the time-separated stochastic mechanics (TSM) is developed to address this problem. We present how the uncertainty of the microscale stresses of a representative volume element and the homogenized macroscale stresses can be approximated with a low number of deterministic finite element simulations. Quantities of interest are the expectation, standard deviation, and the probability distribution function of the stresses on micro- and macroscale. The results showcase that the TSM is able to approximate the reference results very well at a minimal fraction of the computational cost needed for Monte Carlo simulations.",
keywords = "Composite materials, Computational homogenization, Time-separated stochastic mechanics, Uncertain material parameters",
author = "Hendrik Geisler and Philipp Junker",
note = "Funding Information: The authors thank J. Nagel for his guidance. This work has been supported by the German Research Foundation (DFG), Germany within the framework of the international research training group IRTG 2657 {\textquoteleft}{\textquoteleft}Computational Mechanics Techniques in High Dimensions{\textquoteright}{\textquoteright} (Reference: GRK 2657/1, Project number 433082294). ",
year = "2024",
month = apr,
doi = "10.1016/j.probengmech.2024.103618",
language = "English",
volume = "76",
journal = "Probabilistic Engineering Mechanics",
issn = "0266-8920",
publisher = "Elsevier Ltd.",
}