3D Dynamic Crack under Cyclic Loading using XFEM

Numerical Treatment

authored by: Tengfei Lyu, Stefan Löhnert, Peter Wriggers
Abstract: The eXtended Finite Element Method (XFEM) is a special numerical method to handle arbitrary discontinuities in the displacement field independent of the finite element mesh. This is advantageous during crack initiation, growth and propagation processes. In the range of continuum damage mechanics, gradient-enhanced damage models can be used to model damage and fracture without spurious mesh dependencies. Gradient-enhanced damage models have been investigated extensively in the context of quasi-brittle and elasto-plastic materials. To avoid fracture and failure of materials, modelling the component under cyclic loading is significant for fatigue lifetime prediction. The focus of this contribution is set on algorithmic issues. The numerical treatment of 3d cracks under cyclic loading is investigated. The domain is discretized with ten-node tetrahedral elements. Discrete cracks are captured using XFEM and updated by level set methods. In oder to take advantage of the explicit time discretization scheme, a modified differential equation for the gradient-enhanced damage is presented and the central difference explicit time stepping method is employed to obtain 2nd oder accuracy of the solved equations.
Organisation(s): Institute of Continuum Mechanics
External Organisation(s): Technische Universität Dresden
Type: Article
Journal: PAMM - Proceedings in Applied Mathematics and Mechanics
Volume: 19
No. of pages: 2
ISSN: 1617-7061
Publication date: 18.11.2019
Publication status: Published
Electronic version(s): https://doi.org/10.1002/pamm.201900147 (Access: Open)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{8078597c3a264daaa5e0535655608fa1,
title = "3D Dynamic Crack under Cyclic Loading using XFEM: Numerical Treatment",
abstract = "The eXtended Finite Element Method (XFEM) is a special numerical method to handle arbitrary discontinuities in the displacement field independent of the finite element mesh. This is advantageous during crack initiation, growth and propagation processes. In the range of continuum damage mechanics, gradient-enhanced damage models can be used to model damage and fracture without spurious mesh dependencies. Gradient-enhanced damage models have been investigated extensively in the context of quasi-brittle and elasto-plastic materials. To avoid fracture and failure of materials, modelling the component under cyclic loading is significant for fatigue lifetime prediction. The focus of this contribution is set on algorithmic issues. The numerical treatment of 3d cracks under cyclic loading is investigated. The domain is discretized with ten-node tetrahedral elements. Discrete cracks are captured using XFEM and updated by level set methods. In oder to take advantage of the explicit time discretization scheme, a modified differential equation for the gradient-enhanced damage is presented and the central difference explicit time stepping method is employed to obtain 2nd oder accuracy of the solved equations.",
author = "Tengfei Lyu and Stefan L{\"o}hnert and Peter Wriggers",
note = "Funding information: The support of this research within the Collaborative Research Center SFB/Transregio 73 by the German ResearchFoundation is gratefully acknowledged.; 90th Annual Meeting of the International Association of Applied Mathematics and Mechanics (GAMM) ; Conference date: 18-02-2019 Through 22-02-2019",
year = "2019",
month = nov,
day = "18",
doi = "10.1002/pamm.201900147",
language = "English",
volume = "19",
journal = "PAMM - Proceedings in Applied Mathematics and Mechanics",
issn = "1617-7061",
publisher = "Wiley Online Library",
number = "1",
}