Phase-field modeling of brittle fracture using an efficient virtual element scheme

authored by: Fadi Aldakheel, Blaž Hudobivnik, Ali Hussein, Peter Wriggers
Abstract: This work addresses an efficient low order virtual element method (VEM) for the phase-field modeling of isotropic brittle fracture. Virtual elements were introduced in the last decade and applied to various problems in solid mechanics. The phase-field approach regularizes sharp crack surfaces within a pure continuum setting by a specific gradient damage modeling with constitutive terms rooted in fracture mechanics, see Miehe et al. [23] and Miehe et al. [29]. In the presented contribution, we propose a rigorous variational-based framework for the phase-field modeling of brittle fracture in elastic solids undergoing small strains. The key goal here, is the extension towards the recently developed virtual element formulation due to the flexible choice of nodes number in an element which can be changed easily during the simulation process, as outlined in Wriggers et al. [11] and Wriggers et al. [18]. To this end, the potential density is formulated in terms of suitable polynomial functions, instead of computing the unknown shape functions for complicated element geometries, e.g. arbitrary convex or concave polygonal elements. An important aspect of this work is the introduction of an incremental minimization principle, with a novel construction of the stabilization density for the coupled multi-field problem. On the computational side, a robust and efficient monolithic scheme is employed using the software tool ACEFEM program in the numerical implementation to compute the unknowns (displacement and crack phase-field), see Korelc and Wriggers [52]. The performance of the formulation is underlined by means of representative examples.
Organisation(s): Institute of Continuum Mechanics
Type: Article
Journal: Computer Methods in Applied Mechanics and Engineering
Volume: 341
Pages: 443-466
No. of pages: 24
ISSN: 0045-7825
Publication date: 01.11.2018
Publication status: Published
Peer reviewed: Yes
ASJC Scopus subject areas: Computational Mechanics, Mechanics of Materials, Mechanical Engineering, Physics and Astronomy(all), Computer Science Applications
Electronic version(s): https://doi.org/10.1016/j.cma.2018.07.008 (Access: Closed)
: Details in the research portal "Research@Leibniz University"

BibTeX

@article{a9c37cad4f6142239d9e3d9467eb2c54,
title = "Phase-field modeling of brittle fracture using an efficient virtual element scheme",
abstract = "This work addresses an efficient low order virtual element method (VEM) for the phase-field modeling of isotropic brittle fracture. Virtual elements were introduced in the last decade and applied to various problems in solid mechanics. The phase-field approach regularizes sharp crack surfaces within a pure continuum setting by a specific gradient damage modeling with constitutive terms rooted in fracture mechanics, see Miehe et al. [23] and Miehe et al. [29]. In the presented contribution, we propose a rigorous variational-based framework for the phase-field modeling of brittle fracture in elastic solids undergoing small strains. The key goal here, is the extension towards the recently developed virtual element formulation due to the flexible choice of nodes number in an element which can be changed easily during the simulation process, as outlined in Wriggers et al. [11] and Wriggers et al. [18]. To this end, the potential density is formulated in terms of suitable polynomial functions, instead of computing the unknown shape functions for complicated element geometries, e.g. arbitrary convex or concave polygonal elements. An important aspect of this work is the introduction of an incremental minimization principle, with a novel construction of the stabilization density for the coupled multi-field problem. On the computational side, a robust and efficient monolithic scheme is employed using the software tool ACEFEM program in the numerical implementation to compute the unknowns (displacement and crack phase-field), see Korelc and Wriggers [52]. The performance of the formulation is underlined by means of representative examples.",
keywords = "Brittle fracture, Phase-field modeling, Stabilization, Virtual element method (VEM)",
author = "Fadi Aldakheel and Bla{\v z} Hudobivnik and Ali Hussein and Peter Wriggers",
note = "Funding information: The corresponding authors gratefully acknowledgesupport for this research by (i) the collaborative research center CRC 1153 “ Process chain for the production of hybrid high-performance components through tailored forming ”, (ii) the “German Research Foundation” (DFG) in the Priority Program SPP 2020 under the project WR 19/58-1 and (iii) the Deutsche Forschungsgemeinschaft in the Priority Program 1748 “ Reliable simulation techniques in solid mechanics: Development of non- standard discretization methods, mechanical and mathematical analysis ” under the project WR 19/50-1 .",
year = "2018",
month = nov,
day = "1",
doi = "10.1016/j.cma.2018.07.008",
language = "English",
volume = "341",
pages = "443--466",
journal = "Computer Methods in Applied Mechanics and Engineering",
issn = "0045-7825",
publisher = "Elsevier",
}