Time-separated stochastic mechanics for the simulation of viscoelastic structures with local random material fluctuations

authored by: Hendrik Geisler, Philipp Junker
Abstract: Simulating structures with history-dependent material models and uncertain material parameters is often computationally expensive. In contrast, the time-separated stochastic mechanics (TSM) has proven to provide an efficient yet accurate method for the computation of stochastic visco-elastic materials. In this work, the TSM is extended for viscoelastic structures with local random material fluctuations. The time-separated stochastic mechanics is based on a separation of the stochastic viscous evolution equation in time-dependent deterministic and time-independent stochastic terms enabling an efficient implementation. Here, the method is expanded by the Karhunen–Loéve expansion for the representation of the random fields of the material parameters. The method requires a low number of deterministic FEM simulations to approximate stress and reaction force, thus remarkably reducing the computational effort compared to classical Monte Carlo simulations. Multiple numerical simulations are presented to study accuracy, robustness and efficiency of the developed method.
Organisation(s): Institute of Continuum Mechanics
International RTG 2657: Computational Mechanics Techniques in High Dimensions
Type: Article
Journal: Computer Methods in Applied Mechanics and Engineering
Volume: 407
ISSN: 0045-7825
Publication date: 15.03.2023
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Computational Mechanics, Mechanics of Materials, Mechanical Engineering, Physics and Astronomy(all), Computer Science Applications
Electronic version(s): https://doi.org/10.1016/j.cma.2023.115916 (Access: Closed)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{24ca91a636814944bf1651f1c4bd7f24,
title = "Time-separated stochastic mechanics for the simulation of viscoelastic structures with local random material fluctuations",
abstract = "Simulating structures with history-dependent material models and uncertain material parameters is often computationally expensive. In contrast, the time-separated stochastic mechanics (TSM) has proven to provide an efficient yet accurate method for the computation of stochastic visco-elastic materials. In this work, the TSM is extended for viscoelastic structures with local random material fluctuations. The time-separated stochastic mechanics is based on a separation of the stochastic viscous evolution equation in time-dependent deterministic and time-independent stochastic terms enabling an efficient implementation. Here, the method is expanded by the Karhunen–Lo{\'e}ve expansion for the representation of the random fields of the material parameters. The method requires a low number of deterministic FEM simulations to approximate stress and reaction force, thus remarkably reducing the computational effort compared to classical Monte Carlo simulations. Multiple numerical simulations are presented to study accuracy, robustness and efficiency of the developed method.",
keywords = "Karhunen–Lo{\'e}ve expansion, Random fields, Stochastic viscoelastic material, Time-separated stochastic mechanics",
author = "Hendrik Geisler and Philipp Junker",
note = "Funding Information: This work has been supported by the German Research Foundation (DFG) within the framework of the International Research Training Group IRTG 2657 “Computational Mechanics Techniques in High Dimensions” (Reference: GRK 2657/1 - Project number 433082294 ). This work was further supported by the LUH compute cluster, which is funded by the Leibniz University of Hannover , the Lower Saxony Ministry of Science and Culture (MWK), Germany and the German Research Foundation (DFG) . ",
year = "2023",
month = mar,
day = "15",
doi = "10.1016/j.cma.2023.115916",
language = "English",
volume = "407",
journal = "Computer Methods in Applied Mechanics and Engineering",
issn = "0045-7825",
publisher = "Elsevier",
}