A unified phase-field theory for the mechanics of damage and quasi-brittle failure

Wu, Jian‐Ying

doi:10.1016/j.jmps.2017.03.015

Cited by 606 publications

(346 citation statements)

References 40 publications

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“…There is a large literature devoted to the analysis of the robustness of quasi-Newton methods when dealing with non-convex minimization problems -see, e.g., [27][28][29] and references therein. Very recently, Wu et al [30] showed the potential of quasi-Newton monolithic approaches in the context of the so-called unified phase field damage theory, a phase field regularisation of cohesive zone models (PF-CZM) [31,32]. We extend their analysis to the standard phase field fracture formulation and showcase the potential of the method in three problems of different nature: quasi-static fracture, phase field fatigue and dynamic fracture.…”

Section: Introductionmentioning

confidence: 89%

Phase field fracture modelling using quasi-Newton methods and a new adaptive step scheme

Kristensen

Martínez‐Pañeda

2020

Theoretical and Applied Fracture Mechanics

183

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We investigate the potential of quasi-Newton methods in facilitating convergence of monolithic solution schemes for phase field fracture modelling. Several paradigmatic boundary value problems are addressed, spanning the fields of quasi-static fracture, fatigue damage and dynamic cracking. The finite element results obtained reveal the robustness of quasi-Newton monolithic schemes, with convergence readily attained under both stable and unstable cracking conditions. Moreover, since the solution method is unconditionally stable, very significant computational gains are observed relative to the widely used staggered solution schemes. In addition, a new adaptive time increment scheme is presented to further reduces the computational cost while allowing to accurately resolve sudden changes in material behavior, such as unstable crack growth. Computation times can be reduced by several orders of magnitude, with the number of load increments required by the corresponding staggered solution being up to 3000 times higher. Quasi-Newton monolithic solution schemes can be a key enabler for large scale phase field fracture simulations. Implications are particularly relevant for the emerging field of phase field fatigue, as results show that staggered cycle-by-cycle calculations are prohibitive in mid or high cycle fatigue. The finite element codes are available to download from www.empaneda.com/codes.

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Section: Introductionmentioning

confidence: 89%

Phase field fracture modelling using quasi-Newton methods and a new adaptive step scheme

Kristensen

Martínez‐Pañeda

2020

Theoretical and Applied Fracture Mechanics

183

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“…One of the main ingredients for the outstanding progresses on phase field methods stems from the fact that this variational approach does offer very appealing aspects and can easily be implemented into multi-field finite element frameworks. In view of the strong potential of the phase field methods, recent developments encompassed its application to cohesive-like fracture (Verhoosel and de Borst, 2013), coupled damage-plasticity (Ambati et al, 2015;Miehe et al, 2015aMiehe et al, , 2016, shells (Miehe et al, 2014;Areias et al, 2016;Reinoso et al, 2017b), thermo-elastic (Miehe et al, 2015b) and hydrogen embrittlement (Martínez-Pañeda et al, 2018) applications, defining alternative degradation functions (Wu, 2017;Sargado et al, 2017), among many others. Owing to its modular formulation, the phase-field approach to fracture has proven to be a powerful tool for fracture characterization of many different materials such as arterial walls (Gültekin et al, 2018), and anisotropic media (Teichtmeister et al, 2017;Bleyer and Alessi, 2018;Quintanas-Corominas et al, 2019), to quote a few of them.…”

Section: Introductionmentioning

confidence: 99%

A phase field approach for damage propagation in periodic microstructured materials

et al. 2019

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In the present work, the evolution of damage in periodic composite materials is investigated through a novel finite element-based multiscale computational approach. The methodology is developed by means of the original combination of homogenization methods with the phase field approach of fracture. This last is applied at the macroscale level on the equivalent homogeneous continuum, whose constitutive properties are obtained in closed form via a two-scale asymptotic homogenization scheme. The formulation allows considering different assumptions on the evolution of damage at the microscale (e.g., damage in the matrix and not in the inclusion/fiber), as well as the role played by the microstructural topology. Numerical results show that the proposed formulation leads to an apparent tensile strength and a postpeak branch of unnotched and notched specimens dependent not only on the internal length scale of the phase field approach, as for homogeneous materials, but also on the inclusion volumetric content and its shape. Down-scaling relations allow the full reconstruction of the microscopic fields at any point of the macroscopic model, as a simple post-processing operation.

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“…In the phase field approach, the initiation and evolution of cracks emerges by solving the partial differential equations of the model, representing its striking feature, which results in a significant simplification of the implementation, especially in 3-D problems. Different versions of the phase field model have been developed and, more importantly, they can be used to model very complex, multiple crack fronts, branching in both 2D and 3D without ad-hoc numerical treatments, i.e., without fracture criteria ( [31,5,27,34,41,13,50,22,69,21]). However, the application of phase field models to study fracture problems in layered media is rather rare in the literature and still open problem.…”

Section: Approach and Objectivementioning

confidence: 99%

Role of interfacial transition zone in phase field modeling of fracture in layered heterogeneous structures

Nguyen

Waldmann

Bui

2019

Journal of Computational Physics

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A B S T R A C TMechanical 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 crackinterface 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 behavior in layered heterogeneous systems under quasi-static load; (b) to introduce a new methodology for better describing interfaces by a regularized interfacial transition zone in the context of variational phase field approach, exploring its important role; (c) to show the accuracy, performance and applicability of the present model in modeling material failure at the interfaces in both 2-D and 3-D bodies; and (d) to quantitatively validate computed crack path with respect to experimental data. Phase field models with both perfectly and cohesive bonded interfaces are thus derived. A regularized interfacial transition zone is introduced to capture characteristics of material mismatch at the interfaces. Numerical examples for 2-D and 3-D layered systems with experimental validation provide fundamentals of fracture behavior in layered structures. The obtained results shed light on the behavior of crack paths, which are drastically affected by the elastic modulus mismatch between two layers and interface types, and reveal the important role of the proposed interfacial transition zone in phase field modeling of crack-interface interactions.

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A unified phase-field theory for the mechanics of damage and quasi-brittle failure

Cited by 606 publications

References 40 publications

Phase field fracture modelling using quasi-Newton methods and a new adaptive step scheme

Phase field fracture modelling using quasi-Newton methods and a new adaptive step scheme

A phase field approach for damage propagation in periodic microstructured materials

Role of interfacial transition zone in phase field modeling of fracture in layered heterogeneous structures

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