Efficient and robust numerical treatment of a gradient-enhanced damage model at large deformations

authored by: Philipp Junker, Johannes Riesselmann, Daniel Balzani
Abstract: The modeling of damage processes in materials constitutes an ill-posed mathematical problem which manifests in mesh-dependent finite element results. The loss of ellipticity of the discrete system of equations is counteracted by regularization schemes of which the gradient enhancement of the strain energy density is often used. In this contribution, we present an extension of the efficient numerical treatment, which has been proposed by Junker et al. in 2019, to materials that are subjected to large deformations. Along with the model derivation, we present a technique for element erosion in the case of severely damaged materials. Efficiency and robustness of our approach is demonstrated by two numerical examples including snapback and springback phenomena.
Organisation(s): Institute of Continuum Mechanics
External Organisation(s): Ruhr-Universität Bochum
Type: Article
Journal: International Journal for Numerical Methods in Engineering
Volume: 123
Pages: 774-793
No. of pages: 20
ISSN: 0029-5981
Publication date: 17.02.2022
Publication status: Published
Peer reviewed: Yes
Electronic version(s): https://doi.org/10.1002/nme.6876 (Access: Open)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{d70c2995bc5a468ebf2da23f4f0d5e7a,
title = "Efficient and robust numerical treatment of a gradient-enhanced damage model at large deformations",
abstract = "The modeling of damage processes in materials constitutes an ill-posed mathematical problem which manifests in mesh-dependent finite element results. The loss of ellipticity of the discrete system of equations is counteracted by regularization schemes of which the gradient enhancement of the strain energy density is often used. In this contribution, we present an extension of the efficient numerical treatment, which has been proposed by Junker et al. in 2019, to materials that are subjected to large deformations. Along with the model derivation, we present a technique for element erosion in the case of severely damaged materials. Efficiency and robustness of our approach is demonstrated by two numerical examples including snapback and springback phenomena.",
author = "Philipp Junker and Johannes Riesselmann and Daniel Balzani",
note = "Funding Information: The authors Johannes Riesselmann and Daniel Balzani greatly appreciate funding by the German Science Foundation (Deutsche Forschungsgemeinschaft, DFG) as part of the Priority Program German 1748 “Reliable simulation techniques in solid mechanics. Development of non‐standard discretization methods, mechanical and mathematical analysis,” project ID BA2823/15‐1.",
year = "2022",
month = feb,
day = "17",
doi = "10.1002/nme.6876",
language = "English",
volume = "123",
pages = "774--793",
journal = "International Journal for Numerical Methods in Engineering",
issn = "0029-5981",
publisher = "John Wiley and Sons Ltd",
number = "3",
}