A new paradigm for the efficient inclusion of stochasticity in engineering simulations

Time-separated stochastic mechanics

authored by: Hendrik Geisler, Cem Erdogan, Jan Nagel, Philipp Junker
Abstract: As a physical fact, randomness is an inherent and ineliminable aspect in all physical measurements and engineering production. As a consequence, material parameters, serving as input data, are only known in a stochastic sense and thus, also output parameters, e.g., stresses, fluctuate. For the estimation of those fluctuations it is imperative to incoporate randomness into engineering simulations. Unfortunately, incorporating uncertain parameters into the modeling and simulation of inelastic materials is often computationally expensive, as many individual simulations may have to be performed. The promise of the proposed method is simple: using extended material models to include stochasticity reduces the number of needed simulations to one. This single computation is cheap, i.e., it has a comparable numerical effort as a single standard simulation. The extended material models are easily derived from standard deterministic material models and account for the effect of uncertainty by an extended set of deterministic material parameters. The time-dependent and stochastic aspects of the material behavior are separated, such that only the deterministic time-dependent behavior of the extended material model needs to be simulated. The effect of stochasticity is then included during post-processing. The feasibility of this approach is demonstrated for three different and highly non-linear material models: viscous damage, viscous phase transformations and elasto-viscoplasticity. A comparison to the Monte Carlo method showcases that the method is indeed able to provide reliable estimates of the expectation and variance of internal variables and stress at a minimal fraction of the computation cost.
Organisation(s): Institute of Continuum Mechanics
External Organisation(s): TU Dortmund University
Type: Article
Journal: Computational mechanics
No. of pages: 25
ISSN: 0178-7675
Publication date: 02.07.2024
Publication status: E-pub ahead of print
Peer reviewed: Yes
ASJC Scopus subject areas: Computational Mechanics, Ocean Engineering, Mechanical Engineering, Computational Theory and Mathematics, Computational Mathematics, Applied Mathematics
Electronic version(s): https://doi.org/10.1007/s00466-024-02500-5 (Access: Open)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{025c570ec41a4170af53581d24099dec,
title = "A new paradigm for the efficient inclusion of stochasticity in engineering simulations: Time-separated stochastic mechanics",
abstract = "As a physical fact, randomness is an inherent and ineliminable aspect in all physical measurements and engineering production. As a consequence, material parameters, serving as input data, are only known in a stochastic sense and thus, also output parameters, e.g., stresses, fluctuate. For the estimation of those fluctuations it is imperative to incoporate randomness into engineering simulations. Unfortunately, incorporating uncertain parameters into the modeling and simulation of inelastic materials is often computationally expensive, as many individual simulations may have to be performed. The promise of the proposed method is simple: using extended material models to include stochasticity reduces the number of needed simulations to one. This single computation is cheap, i.e., it has a comparable numerical effort as a single standard simulation. The extended material models are easily derived from standard deterministic material models and account for the effect of uncertainty by an extended set of deterministic material parameters. The time-dependent and stochastic aspects of the material behavior are separated, such that only the deterministic time-dependent behavior of the extended material model needs to be simulated. The effect of stochasticity is then included during post-processing. The feasibility of this approach is demonstrated for three different and highly non-linear material models: viscous damage, viscous phase transformations and elasto-viscoplasticity. A comparison to the Monte Carlo method showcases that the method is indeed able to provide reliable estimates of the expectation and variance of internal variables and stress at a minimal fraction of the computation cost.",
keywords = "Inelasticity, Time-separated stochastic mechanics, Uncertainty",
author = "Hendrik Geisler and Cem Erdogan and Jan Nagel and Philipp Junker",
note = "Publisher Copyright: {\textcopyright} The Author(s) 2024.",
year = "2024",
month = jul,
day = "2",
doi = "10.1007/s00466-024-02500-5",
language = "English",
journal = "Computational mechanics",
issn = "0178-7675",
publisher = "Springer Verlag",
}