Error controlled adaptive multiscale XFEM simulation of cracks

authored by: S. Loehnert, C. Prange, P. Wriggers
Abstract: The accurate and efficient prediction of the interaction of microcracks with macrocracks has been a challenge for many years. In this paper a discretization error controlled adaptive multiscale technique for the accurate simulation of microstructural effects within a macroscopic component is presented. The simulation of cracks is achieved using the corrected XFEM. The error estimation procedure is based on the well known Zienkiewicz and Zhu method extended to the XFEM for cracks such that physically meaningful stress irregularities and non-smoothnesses are accurately reflected. The incorporation of microstructural features such as microcracks is achieved by means of the multiscale projection method. In this context an error controlled adaptive mesh refinement is performed on the fine scale where microstructural effects may lead to highly complex mechanical behavior. The presented method is applied to a few examples showing its validity and applicability to arbitrary problems within fracture mechanics.
Organisation(s): Institute of Continuum Mechanics
Type: Article
Journal: International journal of fracture
Volume: 178
Pages: 147-156
No. of pages: 10
ISSN: 0376-9429
Publication date: 02.11.2012
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Computational Mechanics, Modelling and Simulation, Mechanics of Materials
Electronic version(s): https://doi.org/10.1007/s10704-012-9777-0 (Access: Unknown)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{f5be9e00c6414e0b8783efb60990f2ee,
title = "Error controlled adaptive multiscale XFEM simulation of cracks",
abstract = "The accurate and efficient prediction of the interaction of microcracks with macrocracks has been a challenge for many years. In this paper a discretization error controlled adaptive multiscale technique for the accurate simulation of microstructural effects within a macroscopic component is presented. The simulation of cracks is achieved using the corrected XFEM. The error estimation procedure is based on the well known Zienkiewicz and Zhu method extended to the XFEM for cracks such that physically meaningful stress irregularities and non-smoothnesses are accurately reflected. The incorporation of microstructural features such as microcracks is achieved by means of the multiscale projection method. In this context an error controlled adaptive mesh refinement is performed on the fine scale where microstructural effects may lead to highly complex mechanical behavior. The presented method is applied to a few examples showing its validity and applicability to arbitrary problems within fracture mechanics.",
keywords = "Cracks, Error estimation, Multiscale, XFEM",
author = "S. Loehnert and C. Prange and P. Wriggers",
note = "Funding information: Acknowledgments The support of the German Research Foundation (DFG) in the frame of the research grant LO 827/3-1 is gratefully acknowledged.",
year = "2012",
month = nov,
day = "2",
doi = "10.1007/s10704-012-9777-0",
language = "English",
volume = "178",
pages = "147--156",
journal = "International journal of fracture",
issn = "0376-9429",
publisher = "Springer Netherlands",
number = "1-2",
}