Details
| Original language | English |
|---|---|
| Pages (from-to) | 1249-1260 |
| Number of pages | 12 |
| Journal | Zeitschrift für angewandte Mathematik und Mechanik |
| Volume | 98 |
| Issue number | 7 |
| Publication status | Published - 11 Apr 2018 |
Abstract
Stochastic fluctuations of material properties, i.e. the elastic constants, result in stochastic fluctuations of the material's response to mechanical loading, i.e. the stresses. In this contribution, we present an analytical approach to the time-efficient and mathematically accurate modeling of the stochastic behavior of visco-elastic materials. The material behavior is modeled using a viscous strain as an internal variable whose evolution is described by a differential equation. Since the stochastic material properties enter the evolution equation, a stochastic differential equation has to be treated which renders the problem rather uncomfortable. However, we present a precise investigation of the problem that yields a treatment similar to the deterministic case but resulting in the analytical estimation both of the expectation value and the variance (and standard deviation) of the stresses. A numerical comparison to Monte Carlo simulations proves the reliability of our approach.
Keywords
- analytical solution, energy relaxation, stochastic material behavior, stress expectation and variance, visco-elastic material
ASJC Scopus subject areas
- Engineering(all)
- Computational Mechanics
- Mathematics(all)
- Applied Mathematics
Cite this
- Standard
- Harvard
- Apa
- Vancouver
- BibTeX
- RIS
In: Zeitschrift für angewandte Mathematik und Mechanik, Vol. 98, No. 7, 11.04.2018, p. 1249-1260.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - An analytical approach to modeling the stochastic behavior of visco-elastic materials
AU - Junker, Philipp
AU - Nagel, Jan
N1 - Publisher Copyright: © 2018 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim
PY - 2018/4/11
Y1 - 2018/4/11
N2 - Stochastic fluctuations of material properties, i.e. the elastic constants, result in stochastic fluctuations of the material's response to mechanical loading, i.e. the stresses. In this contribution, we present an analytical approach to the time-efficient and mathematically accurate modeling of the stochastic behavior of visco-elastic materials. The material behavior is modeled using a viscous strain as an internal variable whose evolution is described by a differential equation. Since the stochastic material properties enter the evolution equation, a stochastic differential equation has to be treated which renders the problem rather uncomfortable. However, we present a precise investigation of the problem that yields a treatment similar to the deterministic case but resulting in the analytical estimation both of the expectation value and the variance (and standard deviation) of the stresses. A numerical comparison to Monte Carlo simulations proves the reliability of our approach.
AB - Stochastic fluctuations of material properties, i.e. the elastic constants, result in stochastic fluctuations of the material's response to mechanical loading, i.e. the stresses. In this contribution, we present an analytical approach to the time-efficient and mathematically accurate modeling of the stochastic behavior of visco-elastic materials. The material behavior is modeled using a viscous strain as an internal variable whose evolution is described by a differential equation. Since the stochastic material properties enter the evolution equation, a stochastic differential equation has to be treated which renders the problem rather uncomfortable. However, we present a precise investigation of the problem that yields a treatment similar to the deterministic case but resulting in the analytical estimation both of the expectation value and the variance (and standard deviation) of the stresses. A numerical comparison to Monte Carlo simulations proves the reliability of our approach.
KW - analytical solution
KW - energy relaxation
KW - stochastic material behavior
KW - stress expectation and variance
KW - visco-elastic material
UR - http://www.scopus.com/inward/record.url?scp=85045334306&partnerID=8YFLogxK
U2 - 10.1002/zamm.201700257
DO - 10.1002/zamm.201700257
M3 - Article
VL - 98
SP - 1249
EP - 1260
JO - Zeitschrift für angewandte Mathematik und Mechanik
JF - Zeitschrift für angewandte Mathematik und Mechanik
SN - 1521-4001
IS - 7
ER -