Dual‐horizon peridynamics

Ren, Huilong; Zhuang, Xiaoying; Cai, Yongchang; Rabczuk, Timon

doi:10.1002/nme.5257

Cited by 617 publications

(171 citation statements)

References 55 publications

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“…As the conventional peridynamics formulation with constant horizon can be viewed as a special case of the DH-PD [26], we here mainly focus on the DH-PD. There are general three types of peridynamics, as shown in Fig.…”

Section: Dual-horizon Peridynamicsmentioning

confidence: 99%

Dual-horizon peridynamics: A stable solution to varying horizons

Ren

Zhuang

Rabczuk

2017

Computer Methods in Applied Mechanics and Engineering

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565

105

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In this paper, we present a dual-horizon peridynamics formulation which allows for simulations with dual-horizon with minimal spurious wave reflection. We prove the general dual property for dual-horizon peridynamics, based on which the balance of momentum and angular momentum in PD are naturally satisfied. We also analyze the crack pattern of random point distribution and the multiple materials issue in peridynamics. For selected benchmark problems, we show that DH-PD is less sensitive to the spatial than the original PD formulation.Comment: 21 page

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Section: Dual-horizon Peridynamicsmentioning

confidence: 99%

Dual-horizon peridynamics: A stable solution to varying horizons

Ren

Zhuang

Rabczuk

2017

Computer Methods in Applied Mechanics and Engineering

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565

105

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“…In the OSPD theory, the force vector state is determined by the collective deformation of the family of material points x . The equation of motion of the dual‐horizon OSPD model is given as

ρ ((), x) \cdot bolda ((), boldx, t) = \int_{H_{x}} \underline{T} ([], boldx, t) (⟨⟩, boldp - boldx) normald V_{p} - \int_{H_{x}^{'}} \underline{T} ([], boldp, t) (⟨⟩, boldx - boldp) normald V_{p} + \overset{b}{true} ((), boldx, t),

where ρ ( x ) is the mass density, a ( x , t ) is the acceleration vector, and u ( x , t ) is the displacement vector. V p is the incremental volume associated with node p .

\overset{b}{true} ((), boldx, t)

is the prescribed body force vector, and

\underline{T}

is the force vector state; if the material is simple (a simple material in OSPD is defined as one in which the force state depends only on the deformation state), the force state does not depend explicitly on time t .…”

Section: Linearization Of Dual‐horizon Ospdmentioning

confidence: 99%

An implicit dual‐based approach to couple peridynamics with classical continuum mechanics

Bie

She

et al. 2019

Numerical Meth Engineering

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Summary A general local/nonlocal implicit coupling technique called the dual‐based approach is proposed to couple peridynamics (PD) with classical continuum mechanics. In the present method, physical information is transmitted mutually from local to nonlocal regions through the coupling elements; no transition region is introduced. For different mesh discretizations, two coupling methods are achieved with simplicity and effectivity. To obtain the stiffness matrix of the coupled model, without loss of generality, the implicit dual‐horizon ordinary state‐based peridynamic model is proposed, in which the linearization of dual‐horizon ordinary state‐based PD is derived and the dual assembly algorithm of the peridynamic stiffness matrix is developed. It will be seen that the implicit dual‐based coupling approach provides a new implicit coupling method that is easy to implement and makes full use of the internal connection between PD and classical continuum mechanics. Several numerical examples involving static crack propagation are investigated, and the satisfactory results show both quantitative and qualitative agreement with either the analytic solution or the available experiment.

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“…Background cells with large errors are divided following a quad‐tree structure in 2D and an octree structure in 3D . New particles are added at the vertices of the divided cells in the same way as a recent adaptivity approach for peridynamics, but a difference lies in the triggers for adaptive refinement. In the proposed method, refinement is applied to background cells with large errors estimated by Equation , whereas the refinement in the peridynamics approach is activated when the density of potential energy exceeds a predefined threshold value.…”

Section: A Modified Cpm For Linear Elastic Fracture Mechanicsmentioning

confidence: 99%

“…New particles are added at the vertices of the divided cells in the same way as a recent adaptivity approach for peridynamics, but a difference lies in the triggers for adaptive refinement. In the proposed method, refinement is applied to background cells with large errors estimated by Equation , whereas the refinement in the peridynamics approach is activated when the density of potential energy exceeds a predefined threshold value. The difference is because the proposed CPM is based on the weak form of governing equations, whereas peridynamics makes use of the strong form.…”

Section: A Modified Cpm For Linear Elastic Fracture Mechanicsmentioning

confidence: 99%

An adaptive cracking particle method providing explicit and accurate description of 3D crack surfaces

Augarde

2018

Numerical Meth Engineering

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Summary Cracks in 3‐dimensions (3D) have arbitrary shapes and therefore present difficulties for numerical modelling. A novel adaptive cracking particle method with explicit and accurate description of 3D cracks is described in this paper. In this meshless method, crack surfaces are described by a set of discontinuous segments, which are associated with particles. This group of particles are assumed all to be “cracked” and split into 2 subparticles with modified support domains. Compared to the original method where the spherical supports at particles are equally divided, the proposed method makes use of nonplanar segments to account for changes in crack face direction. The orientations of those segments and the angular changes of cracks during crack propagation steps are recorded using triangular meshes. Supports of weight functions are modified according to those changes so that quasi‐continuous crack surfaces can be obtained, avoiding the spurious cracking seen in earlier cracking particle methods. An adaptive approach in 3D is then introduced to capture stress gradients around crack fronts. Several 3D crack problems with reference results have been tested to validate the proposed method with good agreement being achieved using the new method, showing it to be potentially a significant advance for 3D fracture prediction problems.

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Dual‐horizon peridynamics

Cited by 617 publications

References 55 publications

Dual-horizon peridynamics: A stable solution to varying horizons

Dual-horizon peridynamics: A stable solution to varying horizons

An implicit dual‐based approach to couple peridynamics with classical continuum mechanics

An adaptive cracking particle method providing explicit and accurate description of 3D crack surfaces

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