Analysis of dynamic crack propagation in two-dimensional elastic bodies by coupling the boundary element method and the bond-based peridynamics

Yang, Yang; Liu, Yijun

doi:10.1016/j.cma.2022.115339

Cited by 16 publications

(3 citation statements)

References 28 publications

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“…Several coupled numerical methods have been proposed based on the fundamental numerical approaches mentioned above. For example, to enhance computational efficiency, PD-MPM is coupled with numerical methods of classical continuum mechanics [22][23][24][25][26]. These coupled methods essentially integrate two types of continuum mechanical media: the PD medium and the classical continuum medium.…”

Section: Introductionmentioning

confidence: 99%

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The Boundary Element Method for Ordinary State-Based Peridynamics

Liang,

Wang

2024

CMES

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The peridynamics (PD), as a promising nonlocal continuum mechanics theory, shines in solving discontinuous problems. Up to now, various numerical methods, such as the peridynamic mesh-free particle method (PD-MPM), peridynamic finite element method (PD-FEM), and peridynamic boundary element method (PD-BEM), have been proposed. PD-BEM, in particular, outperforms other methods by eliminating spurious boundary softening, efficiently handling infinite problems, and ensuring high computational accuracy. However, the existing PD-BEM is constructed exclusively for bond-based peridynamics (BBPD) with fixed Poisson's ratio, limiting its applicability to crack propagation problems and scenarios involving infinite or semi-infinite problems. In this paper, we address these limitations by introducing the boundary element method (BEM) for ordinary state-based peridynamics (OSPD-BEM). Additionally, we present a crack propagation model embedded within the framework of OSPD-BEM to simulate crack propagations. To validate the effectiveness of OSPD-BEM, we conduct four numerical examples: deformation under uniaxial loading, crack initiation in a double-notched specimen, wedge-splitting test, and threepoint bending test. The results demonstrate the accuracy and efficiency of OSPD-BEM, highlighting its capability to successfully eliminate spurious boundary softening phenomena under varying Poisson's ratios. Moreover, OSPD-BEM significantly reduces computational time and exhibits greater consistency with experimental results compared to PD-MPM.

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Section: Introductionmentioning

confidence: 99%

“…It is worth clarifying the term "PD-BEM" to avoid misunderstandings. PD-BEM is a numerical method constructed based on peridynamic theory, differing from numerical methods that combine the classical local continuum theory's Boundary Element Method (BEM) with the mesh-free particle method based on peridynamic theory [25][26][27][28].…”

Section: Introductionmentioning

confidence: 99%

The Boundary Element Method for Ordinary State-Based Peridynamics

Liang,

Wang

2024

CMES

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“…The crack inversion based on numerical technique includes forward analysis and objective function minimization. Numerical methods which can be used for forward analysis include finite element method [1][2][3], meshless method [4][5][6], boundary element method [7][8][9][10], and XFEM [11][12][13], etc. The traditional finite element method relies too much on mesh, and the mesh needs to be re-divided in each iteration.…”

Section: Introductionmentioning

confidence: 99%

A combination of extended finite element method and the Kriging model based crack identification method

Xie,

Zhao,

et al. 2023

Phys. Scr.

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In this paper, we proposed a crack identification method in which the extended finite element method (XFEM) and a surrogate model are employed. The XFEM is used for accurate modeling of fractures, while the employment of Latin hypercube sampling (LHS) ensures a representative sample space for the input parameters. Then, we use a Kriging surrogate model to establish the response surface between the input and output data and to verify the accuracy of the model predictions. The Kriging model is based on a Gaussian process that models the correlation between the sample points, and it provides an efficient way to interpolate between known data points. To find the optimal solution, we combine the Kriging surrogate model with the particle swarm optimization (PSO) algorithm. From the numerical examples, it can be found that the optimal solutions are in good agreement with the exact solutions.

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