Multilevel global–local techniques for adaptive ductile phase-field fracture

authored by: Fadi Aldakheel, Nima Noii, Thomas Wick, Olivier Allix, Peter Wriggers
Abstract: This paper outlines a rigorous variational-based multilevel Global-Local formulation for ductile fracture. Here, a phase-field formulation is used to resolve failure mechanisms by regularizing the sharp crack topology on the local state. The coupling of plasticity to the crack phase-field is realized by a constitutive work density function, which is characterized through a degraded stored elastic energy and the accumulated dissipated energy due to plasticity and damage. Two different Global-Local approaches based on the idea of multiplicative Schwarz' alternating method are proposed: (i) A global constitutive model with an elastic-plastic behavior is first proposed, while it is enhanced with a single local domain, which, in turn, describes an elastic-plastic fracturing response. (ii) The main objective of the second model is to introduce an adoption of the Global-Local approach toward the multilevel local setting. To this end, an elastic-plastic global constitutive model is augmented with two distinct local domains; in which, the first local domain behaves as an elastic-plastic material and the next local domain is modeled due to the fracture state. To further reduce the computational cost, predictor-corrector adaptivity within Global-Local concept is introduced. An adaptive scheme is devised through the evolution of the effective global plastic flow (for only elastic-plastic adaptivity), and through the evolution of the local crack phase-field state (for only fracture adaptivity). Thus, two local domains are dynamically updated during the computation, resulting with two-way adaptivity procedure. The overall response of the Global-Local approach in terms of accuracy/robustness and efficiency is verified using single-scale problems. The resulting framework is algorithmically described in detail and substantiated with numerical examples.
Organisation(s): Institute of Continuum Mechanics
Institute of Applied Mathematics
PhoenixD: Photonics, Optics, and Engineering - Innovation Across Disciplines
External Organisation(s): Université Paris-Saclay
École normale supérieure Paris-Saclay (ENS Paris-Saclay)
Centre national de la recherche scientifique (CNRS)
Type: Article
Journal: Computer Methods in Applied Mechanics and Engineering
Volume: 387
ISSN: 0045-7825
Publication date: 15.12.2021
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Computational Mechanics, Mechanics of Materials, Mechanical Engineering, General Physics and Astronomy, Computer Science Applications
Electronic version(s): https://arxiv.org/abs/2103.02377v1 (Access: Open)
https://doi.org/10.1016/j.cma.2021.114175 (Access: Closed)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{3436fe1db2d3412db30ff5f775049ca5,
title = "Multilevel global–local techniques for adaptive ductile phase-field fracture",
abstract = "This paper outlines a rigorous variational-based multilevel Global-Local formulation for ductile fracture. Here, a phase-field formulation is used to resolve failure mechanisms by regularizing the sharp crack topology on the local state. The coupling of plasticity to the crack phase-field is realized by a constitutive work density function, which is characterized through a degraded stored elastic energy and the accumulated dissipated energy due to plasticity and damage. Two different Global-Local approaches based on the idea of multiplicative Schwarz' alternating method are proposed: (i) A global constitutive model with an elastic-plastic behavior is first proposed, while it is enhanced with a single local domain, which, in turn, describes an elastic-plastic fracturing response. (ii) The main objective of the second model is to introduce an adoption of the Global-Local approach toward the multilevel local setting. To this end, an elastic-plastic global constitutive model is augmented with two distinct local domains; in which, the first local domain behaves as an elastic-plastic material and the next local domain is modeled due to the fracture state. To further reduce the computational cost, predictor-corrector adaptivity within Global-Local concept is introduced. An adaptive scheme is devised through the evolution of the effective global plastic flow (for only elastic-plastic adaptivity), and through the evolution of the local crack phase-field state (for only fracture adaptivity). Thus, two local domains are dynamically updated during the computation, resulting with two-way adaptivity procedure. The overall response of the Global-Local approach in terms of accuracy/robustness and efficiency is verified using single-scale problems. The resulting framework is algorithmically described in detail and substantiated with numerical examples. ",
keywords = "Dual mortar method, Ductile failure, Mesh adaptivity, Multilevel global–local method, Phase-field approach",
author = "Fadi Aldakheel and Nima Noii and Thomas Wick and Olivier Allix and Peter Wriggers",
note = "Funding Information: F. Aldakheel and N. Noii were founded by the Priority Program, Germany DFG-SPP 2020 within its second funding phase. T. Wick and P. Wriggers were funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) under Germany{\textquoteright}s Excellence Strategy within the Cluster of Excellence PhoenixD, EXC 2122 (project number: 390833453). O. Allix would like to thank the Alexander Foundation for its support through the Gay–Lussac–Humboldt prize which made it possible to closely interact with the colleagues from the Institute of Continuum Mechanics at Leibniz Universit{\"a}t Hannover.",
year = "2021",
month = dec,
day = "15",
doi = "10.1016/j.cma.2021.114175",
language = "English",
volume = "387",
journal = "Computer Methods in Applied Mechanics and Engineering",
issn = "0045-7825",
publisher = "Elsevier",
}