Coupling of an atomistic model and bond-based peridynamic model using an extended Arlequin framework

Zhang, Jieqiong; Han, Fei; Yang, Zihao; Cui, Junzhi

doi:10.1016/j.cma.2022.115663

Cited by 9 publications

(3 citation statements)

References 58 publications

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“…Zheng et al [26] improved the micropolar peridynamics model by considering concrete materials' low tensile strength and high compressive strength and weakened the interaction between rebar and concrete in reinforced concrete structures. Zhang et al [27] and Zheng et al [28] coupled PD with an atomistic (AM) model and classical continuum mechanics (CCM) model, respectively, which guaranteed accuracy and enhanced computational efficiency. Shen et al [29] established a new hybrid model of peridynamics (PD) and finite element method (FEM) based on implicit schemes to improve the computational efficiency.…”

Section: Introductionmentioning

confidence: 99%

Numerical Simulation of Failure Behavior of Reinforced Concrete Shear Walls by a Micropolar Peridynamic Model

Shen

Chen

Zheng³

et al. 2023

Materials

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A reinforced concrete shear wall is an important building structure. Once damage occurs, it not only causes great losses to various properties but also seriously endangers people’s lives. It is difficult to achieve an accurate description of the damage process using the traditional numerical calculation method, which is based on the continuous medium theory. Its bottleneck lies in the crack-induced discontinuity, whereas the adopted numerical analysis method has the continuity requirement. The peridynamic theory can solve discontinuity problems and analyze material damage processes during crack expansion. In this paper, the quasi-static failure and impact failure of shear walls are simulated by improved micropolar peridynamics, which provides the whole process of microdefect growth, damage accumulation, crack initiation, and propagation. The peridynamic predictions are in good match with the current experiment observations, filling the gap of shear wall failure behavior in existing research.

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Section: Introductionmentioning

confidence: 99%

Numerical Simulation of Failure Behavior of Reinforced Concrete Shear Walls by a Micropolar Peridynamic Model

Shen

Chen

Zheng³

et al. 2023

Materials

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“…Inspired by atomistic-to-continuum coupling methods, many techniques for coupling peridynamics with classical continuum mechanics have been developed, including the discrete based coupling approaches, 29,31 the variable horizon approaches 32 and the continuum-based coupling approaches. 28,33 Among them, the continuum-based coupling schemes can be further subdivided into the force-based coupling method, 34,35 the Arlequin coupling method, 33,36 and the Morphing coupling method. 28,37,38 The force-based coupling method presents coupling schemes based on blended governing equations.…”

Section: Introductionmentioning

confidence: 99%

Element‐based coupling modeling of peridynamics and classical continuum mechanics for dynamic brittle fracture

Yu,

Han,

et al. 2023

Numerical Meth Engineering

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In this work, the hybrid peridynamic and classical continuum mechanical model based on the element‐type numerical discretization is used to study the dynamic fracture problem of brittle materials. The weak form of the motion equation for the hybrid model is derived by applying Hamilton's principle. An element‐based spatial discretization scheme is set up using the peridynamics‐based finite element method (PeriFEM) (Han and Li). The ‐convergence and m‐convergence of the hybrid model are analyzed to verify the numerical convergence and the mesh dependency. The influence of the area of the peridynamic model subdomain and the hybrid model subdomain on the calculation efficiency and accuracy is discussed. And the relationship between the crack propagation speed and the crack branching phenomenon is also investigated. Good agreements are obtained by comparing the crack path and the crack speed profile predicted by the hybrid model with those in the literature. Numerical results verify the ability and efficiency of the hybrid model for dynamic fracture problem.

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“…However, the heavy computational burden imposed by the nonlocality of the PD limits the practical applications of these methods. To address this issue, efforts have been made to introduce a class of hybrid methods that utilize PD in areas around a crack and classical mechanics otherwise [32,33,34,35,36,37] and propose fast methods, such as the convolution-based method and the super-fast peridynamic model [38,39,40]. Other works have focused on reducing the computational cost by optimizing the matrix assembly process [41,42] and extending the fast algorithm in molecular dynamics to peridynamic [43], while the theory for uniform regions have been proposed to improve computational efficiency and remove mesh bias effects on crack initiation and propagation [44].…”

Section: Introductionmentioning

confidence: 99%

A fast computational framework for the linear bond-based peridynamic model

Liu,

Tian,

Don

et al. 2023

Preprint

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The non-locality property of peridynamic poses significant computational challenges, especially for problems with discontinuous solutions (e.g., cracks). An efficient matrix-structure-based fast (MSBF) algorithm is proposed for the meshfree method (MF) in solving the linearized bond-based peridynamic models on a rectangular Cartesian computational domain with a uniform mesh. Taking full advantage of the intrinsic Teoplitz structure of the block-diagonal stiffness matrix, the fast Fourier transform (FFT) algorithm is utilized to significantly reduce the number of floating point operations (FLOPS) count to achieve a substantial speed up at fine mesh resolutions than the classical matrix-vector multiplication (MVMP) algorithm. Both methods are applied to multi-dimensional static and dynamic problems, including general boundary conditions and unsteady crack propagation, with good results. The MF-MSBF algorithm demonstrates its substantial computational efficiency with greatly reduced CPU times and smaller memory footprint over the MF-MVMP algorithm in multi-dimensional peridynamic simulations with fine meshes.

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Coupling of an atomistic model and bond-based peridynamic model using an extended Arlequin framework

Cited by 9 publications

References 58 publications

Numerical Simulation of Failure Behavior of Reinforced Concrete Shear Walls by a Micropolar Peridynamic Model

Numerical Simulation of Failure Behavior of Reinforced Concrete Shear Walls by a Micropolar Peridynamic Model

Element‐based coupling modeling of peridynamics and classical continuum mechanics for dynamic brittle fracture

A fast computational framework for the linear bond-based peridynamic model

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