Phase-field modeling of fracture

Published on Jan 1, 2020in Advances in Applied Mechanics9
· DOI :10.1016/BS.AAMS.2019.08.001
Jian-Ying Wu23
Estimated H-index: 23
(SCUT: South China University of Technology),
Vinh Phu Nguyen27
Estimated H-index: 27
(Monash University, Clayton campus)
+ 3 AuthorsStéphane Bordas67
Estimated H-index: 67
(University of Luxembourg)
Sources
Abstract
Abstract Fracture is one of the most commonly encountered failure modes of engineering materials and structures. Prevention of cracking-induced failure is, therefore, a major concern in structural designs. Computational modeling of fracture constitutes an indispensable tool not only to predict the failure of cracking structures but also to shed insights into understanding the fracture processes of many materials such as concrete, rock, ceramic, metals, and biological soft tissues. This chapter provides an extensive overview of the literature on the so-called phase-field fracture/damage models (PFMs), particularly, for quasi-static and dynamic fracture of brittle and quasi-brittle materials, from the points of view of a computational mechanician. PFMs are the regularized versions of the variational approach to fracture which generalizes Griffith's theory for brittle fracture. They can handle topologically complex fractures such as initiation, intersecting, and branching cracks in both two and three dimensions with a quite straightforward implementation. One of our aims is to justify the gaining popularity of PFMs. To this end, both theoretical and computational aspects are discussed and extensive benchmark problems (for quasi-static and dynamic brittle/cohesive fracture) that are successfully and unsuccessfully solved with PFMs are presented. Unresolved issues for further investigations are also documented.
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References369
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#1Jian-Ying Wu (SCUT: South China University of Technology)H-Index: 23
#2Vinh Phu Nguyen (Monash University, Clayton campus)H-Index: 27
Last. Yuli Huang (ARUP Laboratories)H-Index: 8
view all 4 authors...
Abstract In the phase-field modeling of fracture in brittle and quasi-brittle solids, it is crucial to represent the asymmetric tensile/compressive material behavior. Existing phase-field models generally adopt either an intuitive split of the free energy density without capturing the crack boundary conditions properly or an ad hoc hybrid formulation at the loss of variational consistency. To address this issue, this work presents a variationally consistent phase-field anisotropic damage model w...
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#1Anshul Faye (IITs: Indian Institutes of Technology)H-Index: 7
#2Y. Lev (Technion – Israel Institute of Technology)H-Index: 5
Last. Konstantin Y. Volokh (Technion – Israel Institute of Technology)H-Index: 18
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Phase-field or gradient-damage approaches offer elegant ways to model cracks. Material stiffness decreases in the cracked region with the evolution of the phase-field or damage variable. This variable and, consequently, the decreased stiffness are spatially diffused, which essentially means the loss of the internal links and the bearing capacity of the material in a finite region. Considering the loss of material stiffness without the loss of inertial mass seems to be an incomplete idea when dyn...
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#1Tushar Kanti Mandal (Monash University, Clayton campus)H-Index: 8
#2Vinh Phu Nguyen (Monash University, Clayton campus)H-Index: 27
Last. Jian-Ying Wu (SCUT: South China University of Technology)H-Index: 23
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Abstract Being able to seamlessly deal with complex crack patterns like branching, merging and even fragmentation, phase-field models (PFMs) are promising in the computational modeling of fracture of solids. There are, however, some unclear issues such as (i) are phase-field models mesh-bias objective? and (ii) what value should be selected for the length scale parameter? This manuscript provides answers to these practical questions. Three popular PFMs for brittle and cohesive fracture in the li...
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#1Ngoc H. Nguyen (Duy Tan University)H-Index: 3
Modelling brittle fracture by a phase-field fracture formulation has now been widely accepted. However, the full-order phase-field fracture model implemented using finite elements results in a nonlinear coupled system for which simulations are very computationally demanding, particularly for parametrized problems when the randomness and uncertainty of material properties are considered. To tackle this issue, we present two reduced-order phase-field models for parametrized brittle fracture proble...
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#1Thanh Tung Nguyen (University of Luxembourg)H-Index: 16
#2Danièle Waldmann (University of Luxembourg)H-Index: 16
Last. Tinh Quoc Bui (TITech: Tokyo Institute of Technology)H-Index: 57
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Abstract Mechanical behavior of layered materials and structures greatly depends on the mechanical behavior of interfaces. In the past decades, the failure in such layered media has been studied by many researchers due to their critical role in the mechanics and physics of solids. This study aims at investigating crack-interface interaction in two-dimensional (2-D) and three-dimensional (3-D) layered media by a phase field model. Our objectives are fourfold: (a) to better understand fracture beh...
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#1Christian Steinke (TUD: Dresden University of Technology)H-Index: 6
#2Michael Kaliske (TUD: Dresden University of Technology)H-Index: 30
Phase-field crack approximation relies on the proper definition of the crack driving strain energy density to govern the crack evolution and a realistic model for the modified stresses on the crack surface. A novel approach, the directional split, is introduced, analyzed and compared to the two commonly used formulations, which are the spectral split and the volumetric---deviatoric split. The directional split is based on the decomposition of the stress tensor with respect to the crack orientati...
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#1Arne Claus Hansen-Dörr (TUD: Dresden University of Technology)H-Index: 4
#2René de Borst (University of Sheffield)H-Index: 45
Last. Markus Kästner (TUD: Dresden University of Technology)H-Index: 20
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A phase-field approach is proposed for interface failure between two possibly dissimilar materials. The discrete adhesive interface is regularised over a finite width. Due to the use of a regularised crack model for the bulk material, an interaction between the length scales of the crack and the interface can occur. An analytic one-dimensional analysis has been carried out to quantify this effect and a correction is proposed, which compensates influences due to the regularisation in the bulk mat...
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#1Jian-Ying Wu (SCUT: South China University of Technology)H-Index: 23
#2Jie-Feng Qiu (SCUT: South China University of Technology)H-Index: 1
Last. Luo-Jia Zhuang (SCUT: South China University of Technology)H-Index: 1
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Abstract This work addressesnumerical comparison between the extended finite element method (XFEM) and the phase-field regularized cohesive zone model (PF-CZM) (Wu, 2017, 2018a) for the modeling of cohesive fracture induced localized failure in solids. A novel implementation of the PF-CZM is proposed similarly to the XFEM, in which the added degrees of freedom characterizing the crack behavior are associated only with those nodes within a small sub-domain. Representative benchmark examples show ...
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Abstract The phase field approach to brittle fracture is based on smeared energetic representation of sharp fracture into surface. The passage between damaged and undamaged zones is influenced by an internal length scale parameter. In the present paper the approximation of fracture energy in phase field models is studied. Firstly, the diffusion equation of the phase field is numerically investigated. It is demonstrated through simple paradigmatic 2d and 3d cases that the fracture energy during c...
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#1Zhenjun Yang (ZJU: Zhejiang University)H-Index: 34
#2Bei-Bei Li (ZJU: Zhejiang University)H-Index: 1
Last. Jian-Ying Wu (SCUT: South China University of Technology)H-Index: 23
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Abstract Crack nucleation and propagation in concrete is significantly affected by mesoscopic heterogeneities, resulting in distinct failure modes and mechanical behavior. In this work, the phase-field regularized cohesive zone model (PF-CZM) is combined with the X-ray computed tomography (XCT) imaging technique and applied to the modeling of mesoscopic cracking in concrete. More specifically, the in situ XCT image is employed to build the finite element discretization of concrete meso-structure...
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Abstract null null High-speed impact problems usually undergo a form of highly localized plastic deformation under high strain rate with intense shock waves. In this paper, we present a coupled phase field model to simulate fracture in these situations. Our model considers the dynamic finite deformation with both strain hardening and strain rate hardening by the Johnson–Cook plasticity model. In particular, the formulation is posed in an updated Lagrangian framework and the constitutive update i...
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#4Hao Liulei (HIT: Harbin Institute of Technology)
Abstract null null In recent years the phase-field fracture (PFF) model has attracted much attention on failure problems in fiber-reinforced composite materials and structures. However, the discussion on the determination of input parameters remains unsettled. This work aims to seek a general solution for determining the length scale parameter null null null null null l null null null c null null null null null and critical fracture energy density null null null null null g null null null f null...
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Abstract null null null We present a generalised phase field-based formulation for predicting null fatigue crack growth null null in metals. The theoretical framework aims at covering a wide range of null material behaviour . Different fatigue degradation functions are considered and their influence is benchmarked against experiments. The phase field constitutive theory accommodates the so-called null null null AT1 , null AT2 null and phase field-cohesive zone ( PF-CZM null ) models. In regards ...
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#1Jian-Ying Wu (SCUT: South China University of Technology)H-Index: 23
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Abstract null null null null The optimal design, reliable manufacture and durable utilization of electromechanical systems demand objective modeling of failure under coupled electric field and mechanical actions. This is still a challenging and largely an open issue despite the large volumes of contributions from the discontinuous approach and the phase-field community for null brittle fracture . In this work we propose a length scale insensitive phase-field null null cohesive zone model null ( ...
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#1Fadi Aldakheel (Leibniz University of Hanover)H-Index: 21
#2Nima Noii (Leibniz University of Hanover)H-Index: 7
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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-Loca...
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Abstract null null A phase field model for anisotropic, elastoplastic fracture model in layered structures obtained by 3D printing processes is proposed. An extension of anisotropic phase field to elastoplasticity model is developed. The model is able to describe a transition from quasi-brittle to elastoplastic fracture behaviors depending on the angle of layers in the microstructure with respect to the external loading. Such feature is of special interest to describe the anisotropic fracture be...
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#1Wan-Xin Chen (SCUT: South China University of Technology)H-Index: 1
#2Jian-Ying Wu (SCUT: South China University of Technology)H-Index: 23
Abstract null null Despite the popularity of phase-field models for fracture in purely mechanical problems, their application to the modeling of fracture in multi-physics problems is much less reported. This might be attributed, on the one hand, to the theoretical complexity involved in multi-physical phenomena, and on the other hand, to the cumbersome implementation of these coupled models in home-made platforms. In this work, the phase-field cohesive zone model ( PF-CZM ) is adopted as the pro...
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