Numerical simulation of initiation, propagation and coalescence of cracks using the non-ordinary state-based peridynamics

Zhou, Xiaoping; Wang, Yunteng; Xu, Xiaomin

doi:10.1007/s10704-016-0126-6

Cited by 70 publications

(14 citation statements)

References 64 publications

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“…Liu and Hong [174] used discretized PD and parallel computing to study brittle and ductile solids. The first study on dynamic fracture using PD has been presented by Silling [175], for further developments see [138,[176][177][178][179][180][181][182][183] among others. In that context, Shojaei et al [87] coupled finite point method to PD in order to study dynamic fracture.…”

Section: Materials Failurementioning

confidence: 99%

Peridynamics review

Javili

Morasata

Öterkuş

et al. 2018

Mathematics and Mechanics of Solids

214

101

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Peridynamics (PD) is a novel continuum mechanics theory established by Stewart Silling in 2000. The roots of PD can be traced back to the early works of Gabrio Piola according to dell’Isola et al. PD has been attractive to researchers as it is a non-local formulation in an integral form, unlike the local differential form of classical continuum mechanics. Although the method is still in its infancy, the literature on PD is fairly rich and extensive. The prolific growth in PD applications has led to a tremendous number of contributions in various disciplines. This manuscript aims to provide a concise description of the PD theory together with a review of its major applications and related studies in different fields to date. Moreover, we succinctly highlight some lines of research that are yet to be investigated.

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Section: Materials Failurementioning

confidence: 99%

Peridynamics review

Javili

Morasata

Öterkuş

et al. 2018

Mathematics and Mechanics of Solids

214

101

View full text Add to dashboard Cite

show abstract

“…29 With this homogeneous PD model, Zhou and co-authors simulated crack propagation in rocks with pre-existing flaws (e.g. [30][31][32] ). These PD models, when applied to failure of materials with relatively high porosity, would have the same issues as the fully-homogenized PD model discussed in section 5.…”

Section: Literature Reviewmentioning

confidence: 99%

A peridynamic model for damage and fracture in porous materials

Chen¹,

Niazi²,

Bobaru³

2019

Preprint

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(This paper is submitted to "International Journal of Rock Mechanics and Mining Sciences") We introduce a peridynamic (PD) model for simulating damage and fracture in porous materials based on an Intermediate Homogenization (IH) approach. In this approach, instead of explicitly representing the detailed pore geometry, we use homogenization but maintain some information about the microstructure (porosity) in the model. Porosity is introduced in the model as initial peridynamic damage, implemented by stochastically pre-breaking peridynamic bonds to match the desired porosity value. We validate the model for elastodynamics with wave propagation in porous glasses, where we match observed wave propagation speeds and the apparent elastic moduli for various porosities. The model is then used to study the fracture behavior of Berea sandstone under three-point bending loading conditions. We validate the model for fracture problems using the case of failure in a sandstone sample with an off-center pre-notch under three-point bending. The IH-PD results agree very well with experiments: we obtain different failure modes depending on the length of the off-center pre-notch. When the pre-notch is short, most damage (and the subsequent failure) happens in the center of the beam (largest tensile stresses in an un-notched sample). In this case, material porosity makes the fracture behavior “insensitive” to the presence of the off-center pre-notch. When the pre-notch is long, damage starts from near its tip, and progresses in mixed mode towards the loading point. The model captures the location of crack initiation to be the right-corner of the notch, exactly as shown by the experimental acoustic emission results. A fully-homogenized model for the porous sandstone fails to reproduce the failure mode sensitivity on the pre-notch length. The results show the importance of using the IH-PD model when trying to capture the important effects local heterogeneities (like pores) have on damage initiation and growth in porous materials.

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“…Numerical methods can be classified into two categories: continuum‐based methods and discontinuum‐based methods. In terms of the continuum‐based methods, finite element method (FEM), finite difference method (FDM), boundary element method (BEM), extended finite element method (XFEM), phantom node method, strain softening elements, and specific meshfree methods, such as bond particle method (BPM), peridynamics (PD), smoothed particle hydrodynamics (SPH), and general particle dynamics (GPD), were developed to investigate interlayers and crack problems. In terms of the discontinuum‐based methods, distinct lattice spring model (DLSM), discrete element method (DEM), discontinuous deformation analysis (DDA), and numerical manifold method (NMM) were developed.…”

Section: Introductionmentioning

confidence: 99%

Simulation of cracking behaviours in interlayered rocks with flaws subjected to tension using a phase‐field method

Zhou

Jia

Berto

2019

Fatigue Fract Eng Mat Struct

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A phase‐field method (PFM) is used to investigate cracking behaviours, including crack initiation and propagation, in interlayered rocks with preexisting flaws subjected to tension. An example with a bi‐material plate with a centre flaw is used to validate the PFM. Then, numerical simulations of cracking behaviours in interlayered rocks with a single flaw and a cross‐flaw are carried out using PFM. Moreover, the load‐displacement responses are numerically investigated. The PFM numerical results show that the crack propagation trajectories and peak loads of rock specimens depend on the preexisting flaw configuration and the mechanical properties of the interlayers.

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Numerical simulation of initiation, propagation and coalescence of cracks using the non-ordinary state-based peridynamics

Cited by 70 publications

References 64 publications

Peridynamics review

Peridynamics review

A peridynamic model for damage and fracture in porous materials

Simulation of cracking behaviours in interlayered rocks with flaws subjected to tension using a phase‐field method

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