A new paradigm for the efficient inclusion of stochasticity in engineering simulations
Timeseparated stochastic mechanics
 verfasst von
 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 timedependent and stochastic aspects of the material behavior are separated, such that only the deterministic timedependent behavior of the extended material model needs to be simulated. The effect of stochasticity is then included during postprocessing. The feasibility of this approach is demonstrated for three different and highly nonlinear material models: viscous damage, viscous phase transformations and elastoviscoplasticity. 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.
 Organisationseinheit(en)

Institut für Kontinuumsmechanik
 Externe Organisation(en)

Technische Universität Dortmund
 Typ
 Artikel
 Journal
 Computational mechanics
 Anzahl der Seiten
 25
 ISSN
 01787675
 Publikationsdatum
 02.07.2024
 Publikationsstatus
 Elektronisch veröffentlicht (EPub)
 Peerreviewed
 Ja
 ASJC Scopus Sachgebiete
 Numerische Mechanik, Meerestechnik, Maschinenbau, Theoretische Informatik und Mathematik, Computational Mathematics, Angewandte Mathematik
 Elektronische Version(en)

https://doi.org/10.1007/s00466024025005 (Zugang:
Offen)