## Details

Original language | English |
---|---|

Number of pages | 25 |

Journal | Computational mechanics |

Early online date | 2 Jul 2024 |

Publication status | E-pub ahead of print - 2 Jul 2024 |

## 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

## ASJC Scopus subject areas

- Engineering(all)
**Computational Mechanics**- Engineering(all)
**Ocean Engineering**- Engineering(all)
**Mechanical Engineering**- Computer Science(all)
**Computational Theory and Mathematics**- Mathematics(all)
**Computational Mathematics**- Mathematics(all)
**Applied Mathematics**

## Cite this

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- Harvard
- Apa
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**A new paradigm for the efficient inclusion of stochasticity in engineering simulations: Time-separated stochastic mechanics.**/ Geisler, Hendrik; Erdogan, Cem; Nagel, Jan et al.

In: Computational mechanics, 02.07.2024.

Research output: Contribution to journal › Article › Research › peer review

*Computational mechanics*. Advance online publication. https://doi.org/10.1007/s00466-024-02500-5

}

TY - JOUR

T1 - A new paradigm for the efficient inclusion of stochasticity in engineering simulations

T2 - Time-separated stochastic mechanics

AU - Geisler, Hendrik

AU - Erdogan, Cem

AU - Nagel, Jan

AU - Junker, Philipp

N1 - Publisher Copyright: © The Author(s) 2024.

PY - 2024/7/2

Y1 - 2024/7/2

N2 - 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.

AB - 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.

KW - Inelasticity

KW - Time-separated stochastic mechanics

KW - Uncertainty

UR - http://www.scopus.com/inward/record.url?scp=85197304401&partnerID=8YFLogxK

U2 - 10.1007/s00466-024-02500-5

DO - 10.1007/s00466-024-02500-5

M3 - Article

AN - SCOPUS:85197304401

JO - Computational mechanics

JF - Computational mechanics

SN - 0178-7675

ER -