Download this article
Download this article For screen
For printing
Recent Issues

Volume 20, 1 issue

Volume 19, 5 issues

Volume 18, 5 issues

Volume 17, 5 issues

Volume 16, 5 issues

Volume 15, 5 issues

Volume 14, 5 issues

Volume 13, 5 issues

Volume 12, 5 issues

Volume 11, 5 issues

Volume 10, 5 issues

Volume 9, 5 issues

Volume 8, 8 issues

Volume 7, 10 issues

Volume 6, 9 issues

Volume 5, 6 issues

Volume 4, 10 issues

Volume 3, 10 issues

Volume 2, 10 issues

Volume 1, 8 issues

The Journal
About the journal
Ethics and policies
Peer-review process
 
Submission guidelines
Submission form
Editorial board
 
Subscriptions
 
ISSN 1559-3959 (online)
ISSN 1559-3959 (print)
 
Author index
To appear
 
Other MSP journals
Efficient damage simulations under material uncertainties in a weakly intrusive implementation

Hendrik Geisler, Emmanuel Baranger and Philipp Junker
Vol. 20 (2025), No. 1, 15–31
DOI: 10.2140/jomms.2025.20.15
Abstract

Uncertainty quantification is not yet widely adapted in the design process of engineering components despite its importance for achieving sustainable and resource-efficient structures. This is mainly for two reasons:

  • Tracing the effect of uncertainty in engineering simulations is a computationally challenging task. This is especially true for inelastic simulations, as the whole loading history influences the results.

  • Implementations of efficient schemes in standard finite element software are lacking.

In this paper, we tackle both problems. We propose a weakly intrusive implementation of time-separated stochastic mechanics in the finite element software Abaqus. Time-separated stochastic mechanics is an efficient and accurate method for the uncertainty quantification of structures with inelastic material behavior. The method effectively separates the stochastic but time-independent from the deterministic but time-dependent behavior. The resulting scheme consists only two deterministic finite element simulations for homogeneous material fluctuations in order to approximate the stochastic behavior. This brings down the computational cost compared to standard Monte Carlo simulations by at least two orders of magnitude while ensuring accurate solutions. In this paper, the implementation details in Abaqus and numerical comparisons are presented for the example of damage simulations.

Keywords
time-separated stochastic mechanics, weakly intrusive, damage, Abaqus
Milestones
Received: 4 April 2024
Accepted: 26 December 2024
Published: 29 January 2025
Authors
Hendrik Geisler
Institute of Continuum Mechanics
Leibniz University Hannover
Hannover
Germany		 IRTG 2657: Computational Mechanics Techniques in High Dimensions Université Paris-Saclay
CentraleSupélec
ENS Paris-Saclay
CNRS, LMPS - Laboratoire de Mécanique Paris-Saclay
Gif-sur-Yvette, France
Emmanuel Baranger
Université Paris-Saclay, CentraleSupélec, ENS Paris-Saclay, CNRS, LMPS - Laboratoire de Mécanique Paris-Saclay
Avenue des Sciences 4
91190 Gif-sur-Yvette
Germany		 IRTG 2657: Computational Mechanics Techniques in High Dimensions Université Paris-Saclay
CentraleSupélec
ENS Paris-Saclay
CNRS, LMPS - Laboratoire de Mécanique Paris-Saclay
Gif-sur-Yvette, France
Philipp Junker
Institute of Continuum Mechanics
Leibniz University Hannover
Hannover
Germany		 IRTG 2657: Computational Mechanics Techniques in High Dimensions
© 2025 MSP (Mathematical Sciences Publishers).