Details
| Original language | English |
|---|---|
| Pages (from-to) | 308-333 |
| Number of pages | 26 |
| Journal | International Journal for Numerical Methods in Engineering |
| Volume | 121 |
| Issue number | 2 |
| Early online date | 27 Aug 2019 |
| Publication status | Published - 9 Dec 2019 |
| Externally published | Yes |
Abstract
Modeling and simulation of materials with stochastic properties is an emerging field in both mathematics and mechanics. The most important goal is to compute the stochastic characteristics of the random stress, such as the expectation value and the standard deviation. An accurate approach are Monte Carlo simulations; however, they consume drastic computational power due to the large number of stochastic realizations that have to be simulated before convergence is achieved. In this paper, we show that a recently published approach for accurate modeling of viscoelastic materials with stochastic material properties at the material point level in the work of Junker and Nagel is also valid for macroscopic bodies. The method is based on a separation of random but time-invariant variables and time-dependent but deterministic variables for the strain response at the material point (time-separated stochastic mechanics [TSM]). We recall the governing equations, derive a simplified form, and discuss the numerical implementation into a finite element routine. To validate our approach, we compare the TSM simulations with Monte Carlo simulations, which provide the “true” answer but at unaffordable computational costs. In contrast, the numerical effort of our approach is in the same range as for deterministic viscoelastic simulations.
Keywords
- Monte Carlo simulations, finite element method, stochastic material behavior, stress expectation and variance, viscoelastic material
ASJC Scopus subject areas
- Mathematics(all)
- Numerical Analysis
- Engineering(all)
- Mathematics(all)
- Applied Mathematics
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In: International Journal for Numerical Methods in Engineering, Vol. 121, No. 2, 09.12.2019, p. 308-333.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Modeling of viscoelastic structures with random material properties using time‐separated stochastic mechanics
AU - Junker, Philipp
AU - Nagel, Jan
N1 - Publisher Copyright: © 2019 The Authors. International Journal for Numerical Methods in Engineering Published by John Wiley & Sons, Ltd. Copyright: Copyright 2019 Elsevier B.V., All rights reserved.
PY - 2019/12/9
Y1 - 2019/12/9
N2 - Modeling and simulation of materials with stochastic properties is an emerging field in both mathematics and mechanics. The most important goal is to compute the stochastic characteristics of the random stress, such as the expectation value and the standard deviation. An accurate approach are Monte Carlo simulations; however, they consume drastic computational power due to the large number of stochastic realizations that have to be simulated before convergence is achieved. In this paper, we show that a recently published approach for accurate modeling of viscoelastic materials with stochastic material properties at the material point level in the work of Junker and Nagel is also valid for macroscopic bodies. The method is based on a separation of random but time-invariant variables and time-dependent but deterministic variables for the strain response at the material point (time-separated stochastic mechanics [TSM]). We recall the governing equations, derive a simplified form, and discuss the numerical implementation into a finite element routine. To validate our approach, we compare the TSM simulations with Monte Carlo simulations, which provide the “true” answer but at unaffordable computational costs. In contrast, the numerical effort of our approach is in the same range as for deterministic viscoelastic simulations.
AB - Modeling and simulation of materials with stochastic properties is an emerging field in both mathematics and mechanics. The most important goal is to compute the stochastic characteristics of the random stress, such as the expectation value and the standard deviation. An accurate approach are Monte Carlo simulations; however, they consume drastic computational power due to the large number of stochastic realizations that have to be simulated before convergence is achieved. In this paper, we show that a recently published approach for accurate modeling of viscoelastic materials with stochastic material properties at the material point level in the work of Junker and Nagel is also valid for macroscopic bodies. The method is based on a separation of random but time-invariant variables and time-dependent but deterministic variables for the strain response at the material point (time-separated stochastic mechanics [TSM]). We recall the governing equations, derive a simplified form, and discuss the numerical implementation into a finite element routine. To validate our approach, we compare the TSM simulations with Monte Carlo simulations, which provide the “true” answer but at unaffordable computational costs. In contrast, the numerical effort of our approach is in the same range as for deterministic viscoelastic simulations.
KW - Monte Carlo simulations
KW - finite element method
KW - stochastic material behavior
KW - stress expectation and variance
KW - viscoelastic material
UR - http://www.scopus.com/inward/record.url?scp=85074592732&partnerID=8YFLogxK
U2 - 10.1002/nme.6210
DO - 10.1002/nme.6210
M3 - Article
VL - 121
SP - 308
EP - 333
JO - International Journal for Numerical Methods in Engineering
JF - International Journal for Numerical Methods in Engineering
SN - 0029-5981
IS - 2
ER -