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An analytical approach to modeling the stochastic behavior of visco-elastic materials

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

Autorschaft

Externe Organisationen

  • Ruhr-Universität Bochum
  • Eindhoven University of Technology (TU/e)

Details

OriginalspracheEnglisch
Seiten (von - bis)1249-1260
Seitenumfang12
FachzeitschriftZeitschrift für angewandte Mathematik und Mechanik
Jahrgang98
Ausgabenummer7
Frühes Online-Datum11 Apr. 2018
PublikationsstatusVeröffentlicht - 4 Juli 2018
Extern publiziertJa

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.

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An analytical approach to modeling the stochastic behavior of visco-elastic materials. / Junker, Philipp; Nagel, Jan.
in: Zeitschrift für angewandte Mathematik und Mechanik, Jahrgang 98, Nr. 7, 04.07.2018, S. 1249-1260.

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

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AU - Junker, Philipp

AU - Nagel, Jan

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