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

Li, Weidong; Nguyen‐Thanh, Nhon; Zhou, Kun

doi:10.1002/nme.6509

Cited by 50 publications

(3 citation statements)

References 55 publications

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“…Classical Lagrange Galerkin finite elements [146], exponential shape functions [292], isogeometric elements [222], discontinuous finite elements [293], or mixed formulations [283] were mostly utilized for the spatial discretization of the fracture/damage models as described in the previous section. Meshless methods for general phase-field were first introduced in [294] and for meshless phase-field fracture, see e.g., [216,295]. For discretized nonlinear systems, the following solvers are available: alternating minimisation algorithms [146,153,187,237,273,[296][297][298], alternating minimisation algorithm with path-following strategies [299], staggered scheme [186], stabilized staggered schemes [300][301][302][303], monolithic solvers [17,151,290,[304][305][306][307][308], and monolithic solvers with path-following strategies [309,310].…”

Section: Discretization Solvers and Software For Pfmentioning

confidence: 99%

A comparative review of peridynamics and phase-field models for engineering fracture mechanics

et al. 2022

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Computational modeling of the initiation and propagation of complex fracture is central to the discipline of engineering fracture mechanics. This review focuses on two promising approaches: phase-field (PF) and peridynamic (PD) models applied to this class of problems. The basic concepts consisting of constitutive models, failure criteria, discretization schemes, and numerical analysis are briefly summarized for both models. Validation against experimental data is essential for all computational methods to demonstrate predictive accuracy. To that end, the Sandia Fracture Challenge and similar experimental data sets where both models could be benchmarked against are showcased. Emphasis is made to converge on common metrics for the evaluation of these two fracture modeling approaches. Both PD and PF models are assessed in terms of their computational effort and predictive capabilities, with their relative advantages and challenges are summarized.

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Section: Discretization Solvers and Software For Pfmentioning

confidence: 99%

A comparative review of peridynamics and phase-field models for engineering fracture mechanics

et al. 2022

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“…The proposed method may also be used for analysis of contact problems. Future research may focus on analyzing the mechanical behavior of polycrystalline structures [58,59] using the MFS.…”

Section: Figure 6: Rectangular Plate With a Fixed Holementioning

confidence: 99%

The Method of Fundamental Solutions for Two-Dimensional Elastostatic Problems with Stress Concentration and Highly Anisotropic Materials

Hematiyan¹,

Jamshidi²,

Mohammadi³

2022

Computer Modeling in Engineering &Amp; Sciences

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The method of fundamental solutions (MFS) is a boundary-type and truly meshfree method, which is recognized as an efficient numerical tool for solving boundary value problems. The geometrical shape, boundary conditions, and applied loads can be easily modeled in the MFS. This capability makes the MFS particularly suitable for shape optimization, moving load, and inverse problems. However, it is observed that the standard MFS lead to inaccurate solutions for some elastostatic problems with stress concentration and/or highly anisotropic materials. In this work, by a numerical study, the important parameters, which have significant influence on the accuracy of the MFS for the analysis of two-dimensional anisotropic elastostatic problems, are investigated. The studied parameters are the degree of anisotropy of the problem, the ratio of the number of collocation points to the number of source points, and the distance between main and pseudo boundaries. It is observed that as the anisotropy of the material increases, there will be more errors in the results. It is also observed that for simple problems, increasing the distance between main and pseudo boundaries enhances the accuracy of the results; however, it is not the case for complicated problems. Moreover, it is concluded that more collocation points than source points can significantly improve the accuracy of the results.

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“…For example, before ABAQUS launched a version containing the extended finite element method (XFEM), Fang et al [4] had implemented XFEM simulations in it. For other methods that have received widespread attention, such as the cohesive zone model and the phase field model of fracture [5,6], there are also related works in which these methods were implemented in existing software. For example, Lindgaard et al [7] presented a cohesive zone finite element method implemented via user programmable features (UPFs) in ANSYS; and Msekh et al [8][9][10] incorporated the phase field model of fracture with ABAQUS via subroutines.…”

Section: Introductionmentioning

confidence: 99%

ABAQUS and ANSYS Implementations of the Peridynamics-Based Finite Element Method (PeriFEM) for Brittle Fractures

Han¹,

Li²,

Zhang³

et al. 2023

Computer Modeling in Engineering &Amp; Sciences

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In this study, we propose the first unified implementation strategy for peridynamics in commercial finite element method (FEM) software packages based on their application programming interface using the peridynamics-based finite element method (PeriFEM). Using ANSYS and ABAQUS as examples, we present the numerical results and implementation details of PeriFEM in commercial FEM software. PeriFEM is a reformulation of the traditional FEM for solving peridynamic equations numerically. It is considered that the non-local features of peridynamics yet possesses the same computational framework as the traditional FEM. Therefore, this implementation benefits from the consistent computational frameworks of both PeriFEM and the traditional FEM. An implicit algorithm is used for both ANSYS and ABAQUS; however, different convergence criteria are adopted owing to their unique features. In ANSYS, APDL enables users to conveniently obtain broken-bond information from UPFs; thus, the convergence criterion is chosen as no new broken bond. In ABAQUS, obtaining broken-bond information is not convenient for users; thus, the default convergence criterion is used in ABAQUS. The codes integrated into ANSYS and ABAQUS are both verified through benchmark examples, and the computational convergence and costs are compared. The results show that, for some specific examples, ABAQUS is more efficient, whereas the convergence criterion adopted in ANSYS is more robust. Finally, 3D examples are presented to demonstrate the ability of the proposed approach to deal with complex engineering problems.

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

Cited by 50 publications

References 55 publications

A comparative review of peridynamics and phase-field models for engineering fracture mechanics

A comparative review of peridynamics and phase-field models for engineering fracture mechanics

The Method of Fundamental Solutions for Two-Dimensional Elastostatic Problems with Stress Concentration and Highly Anisotropic Materials

ABAQUS and ANSYS Implementations of the Peridynamics-Based Finite Element Method (PeriFEM) for Brittle Fractures

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