Adaptive consistent element-free Galerkin method for phase-field model of brittle fracture

Shao, Yulong; Duan, Qinglin; Qiu, Shasha

doi:10.1007/s00466-019-01679-2

Cited by 56 publications

(20 citation statements)

References 59 publications

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“…It is found that the crack initially twists along the central vertical axis until the crack surface is parallel to the transversal plane, and then grows upwards along the transversal plane until the end of simulations. The simulated crack surface represented by points ( d > 0.9) is visualized in Figure 15 where the crack propagation patterns are in good agreement with reference solutions 36,53,54 . Figure 16 shows the load‐displacement curve for a three‐point bending test.…”

Section: Numerical Examplesmentioning

confidence: 59%

“…The phase‐field variable that is treated as an error estimator can be used to directly determine elements around crack surfaces, whereas the estimator is not efficient for crack initiation 36 . Mesh refinement before crack initiation or growth can give accurate solutions.…”

Section: Adaptive Refinement Strategy For the Phase‐field Modelingmentioning

confidence: 99%

“…Compared to IGA, a meshfree method can conveniently achieve adaptive refinement because it uses a set of scattered nodes for the discretization and field approximation without mesh connectivity. The local maximum‐entropy meshfree method 35 and element‐free Galerkin method 36 were developed for adaptive phase‐field modeling of brittle fracture. In order to incorporate the convenient mesh refinement scheme of a meshfree method into IGA, several approaches have been developed 37,38 .…”

Section: Introductionmentioning

confidence: 99%

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Phase‐field modeling of brittle fracture in a 3D polycrystalline material via an adaptive isogeometric‐meshfreeapproach

Nguyen‐Thanh

Zhou

2020

Numerical Meth Engineering

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Phase-field modeling, which introduces the regularized representation of sharp crack topologies, provides a convenient strategy for tackling 3D fracture problems. In this work, an adaptive isogeometric-meshfree approach is developed for the phase-field modeling of brittle fracture in a 3D polycrystalline material. The isogeometric-meshfree approach uses moving least-squares approximations to construct the equivalence between isogeometric basis functions and meshfree shape functions, thus inheriting the flexible local mesh refinement scheme from a meshfree method. This refinement scheme is improved by introducing an error estimator that includes both the phase field and its gradient. With the present approach, numerical implementations of the adaptive phase-field modeling that introduces the anisotropy of fracture resistance in polycrystals are proposed. In this way, propagating cracks can be dynamically tracked, and the mesh near cracks is refined in a meshfree manner without requiring a priori knowledge of crack paths. Furthermore, the intergranular and transgranular crack propagation patterns in polycrystalline materials can be simulated by the present approach. A series of numerical examples that deal with the isotropic and anisotropic fracture are investigated to demonstrate the robustness and effectiveness of the proposed approach. K E Y W O R D S adaptivity, anisotropy, isogeometric-meshfree approach, phase-field modeling, polycrystalline material 1 INTRODUCTION Fracture behaviors of engineering materials and structures, such as crack initiation, propagation, coalescence, and branching, have been extensively investigated by two types of numerical models: the discrete and diffusive models. The discrete model treats cracks as moving boundaries by constructing discontinuous displacement fields. Within the framework of a discrete model, a variety of methods have been developed, such as the extended finite element method (XFEM), 1 cohesive zone method, 2,3 extended isogeometric analysis (XIGA), 4 and extended meshfree method. 5 As a discrete model requires descriptions of crack surfaces, it suffers from low computational efficiencies induced by the tracking of complex 5042

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Section: Numerical Examplesmentioning

confidence: 59%

Section: Adaptive Refinement Strategy For the Phase‐field Modelingmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Phase‐field modeling of brittle fracture in a 3D polycrystalline material via an adaptive isogeometric‐meshfreeapproach

Nguyen‐Thanh

Zhou

2020

Numerical Meth Engineering

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“…The weak forms introduced in Equation 91or (92) can be further discretised employing either mesh-based, i.e., the FEM, mesh-less methods, see, e.g., [275] or MPM [32]. The resulting discrete equations are then solved in an incremental fashion.…”

Section: Galerkin Approximationmentioning

confidence: 99%

Discrete and Phase Field Methods for Linear Elastic Fracture Mechanics: A Comparative Study and State-of-the-Art Review

et al. 2019

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Three alternative approaches, namely the extended/generalized finite element method (XFEM/GFEM), the scaled boundary finite element method (SBFEM) and phase field methods, are surveyed and compared in the context of linear elastic fracture mechanics (LEFM). The purpose of the study is to provide a critical literature review, emphasizing on the mathematical, conceptual and implementation particularities that lead to the specific advantages and disadvantages of each method, as well as to offer numerical examples that help illustrate these features.

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“…The phase-field variable that is treated as an error estimator can be used directly to determine the elements around crack surfaces, whereas the estimator is not efficient for crack initiation [189]. where lab is the distance between two integration points.…”

Section: Adaptive Mesh Refinementmentioning

confidence: 99%

Isogeometric analysis-based approaches for modeling solid materials and structures with defects

Li¹

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It was a great pleasure working with them in the same research group. The insightful discussions with them are beneficial to this Ph.D. research. My appreciation also extends to Associate Professor Xiao Zhongmin, Associate Professor Idapalapati Sridhar and Dr. Che Faxing for serving on my thesis advisory committee and providing their valuable suggestions. I gratefully acknowledge the Nanyang Technological University for providing me the research scholarship and SMRT-NTU Smart Urban Rail Corporate Laboratory for its continuous support during my Ph.D. study. Last but not least, I would like to express my heartfelt gratitude to my parents and sister for their unconditional love and encouragement.

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Adaptive consistent element-free Galerkin method for phase-field model of brittle fracture

Cited by 56 publications

References 59 publications

Phase‐field modeling of brittle fracture in a 3D polycrystalline material via an adaptive isogeometric‐meshfreeapproach

Phase‐field modeling of brittle fracture in a 3D polycrystalline material via an adaptive isogeometric‐meshfreeapproach

Discrete and Phase Field Methods for Linear Elastic Fracture Mechanics: A Comparative Study and State-of-the-Art Review

Isogeometric analysis-based approaches for modeling solid materials and structures with defects

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