Simulation of the dynamic behavior of viscoelastic structures with random material parameters using time-separated stochastic mechanics

authored by: Hendrik Geisler, Jan Nagel, Philipp Junker
Abstract: Modeling and simulation of materials with stochastic properties is typically computationally expensive, especially for nonlinear materials or dynamic simulations. Time-separated stochastic mechanics (TSM) is a technique to efficiently compute the stochastic characteristics of stress and reaction force of materials. It has successfully been used for viscoelastic materials with random homogenized Young's modulus. The method is based on a decomposition of time-invariant random variables and time-dependent but deterministic variables for the strain response at the material point. In this work, the TSM is extended for the dynamic analysis of stochastic viscoelastic materials. It is showcased that the TSM can efficiently approximate the expectation and variance of the reaction force and the stress for the dynamic simulation of a viscoelastic nonlinear material. Furthermore, generalized equations of the TSM are presented that increase the accuracy and allow for accounting of larger fluctuations of the material parameters. Transient time-domain simulations are performed for different boundary value problems and compared to Monte Carlo simulations to demonstrate the accuracy and computational efficiency of the method.
Organisation(s): Institute of Continuum Mechanics
External Organisation(s): TU Dortmund University
Type: Article
Journal: International Journal of Solids and Structures
Volume: 259
ISSN: 0020-7683
Publication date: 25.12.2022
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Modelling and Simulation, Materials Science(all), Condensed Matter Physics, Mechanics of Materials, Mechanical Engineering, Applied Mathematics
Electronic version(s): https://doi.org/10.1016/j.ijsolstr.2022.112012 (Access: Closed)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{dca30eb02235462687e9a41c6c6922fb,
title = "Simulation of the dynamic behavior of viscoelastic structures with random material parameters using time-separated stochastic mechanics",
abstract = "Modeling and simulation of materials with stochastic properties is typically computationally expensive, especially for nonlinear materials or dynamic simulations. Time-separated stochastic mechanics (TSM) is a technique to efficiently compute the stochastic characteristics of stress and reaction force of materials. It has successfully been used for viscoelastic materials with random homogenized Young's modulus. The method is based on a decomposition of time-invariant random variables and time-dependent but deterministic variables for the strain response at the material point. In this work, the TSM is extended for the dynamic analysis of stochastic viscoelastic materials. It is showcased that the TSM can efficiently approximate the expectation and variance of the reaction force and the stress for the dynamic simulation of a viscoelastic nonlinear material. Furthermore, generalized equations of the TSM are presented that increase the accuracy and allow for accounting of larger fluctuations of the material parameters. Transient time-domain simulations are performed for different boundary value problems and compared to Monte Carlo simulations to demonstrate the accuracy and computational efficiency of the method.",
keywords = "Dynamic behavior, Stochastic viscoelastic material, Time-separated stochastic mechanics",
author = "Hendrik Geisler and Jan Nagel 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). ",
year = "2022",
month = dec,
day = "25",
doi = "10.1016/j.ijsolstr.2022.112012",
language = "English",
volume = "259",
journal = "International Journal of Solids and Structures",
issn = "0020-7683",
publisher = "Elsevier Ltd.",
}