Modelling of Granular Fracture in Polycrystalline Materials Using Ordinary State-Based Peridynamics

Zhu, Ning; Meo, Dennj De; Öterkuş, Erkan

doi:10.3390/ma9120977

Cited by 52 publications

(22 citation statements)

References 45 publications

(53 reference statements)

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“…These errors can be corrected by using surface correction factors and modifying the peridynamic dilatation terms and peridynamic force expressions given in Eqs. (8,9,13,14) as…”

Section: Surface Correctionmentioning

confidence: 99%

“…Since its introduction, there has been a rapid progress in peridynamics research. Since it is a general continuum mechanics formulation, any material system can be analysed by using peridynamics including metals [4], composites [5][6][7], polycrystalline materials [8][9][10], concrete [11], ceramics [12], ice [13], graphene [14], etc. It is also possible to perform fatigue analysis in PD theory [15].…”

Section: Introductionmentioning

confidence: 99%

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Derivation of dual-horizon state-based peridynamics formulation based on Euler–Lagrange equation

Wang

Oterkus

Öterkuş

2020

Continuum Mech. Thermodyn.

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The numerical solution of peridynamics equations is usually done by using uniform spatial discretisation. Although implementation of uniform discretisation is straightforward, it can increase computational time significantly for certain problems. Instead, non-uniform discretisation can be utilised and different discretisation sizes can be used at different parts of the solution domain. Moreover, the peridynamic length scale parameter, horizon, can also vary throughout the solution domain. Such a scenario requires extra attention since conservation laws must be satisfied. To deal with these issues, dual-horizon peridynamics was introduced so that both non-uniform discretisation and variable horizon sizes can be utilised. In this study, dual-horizon peridynamics formulation is derived by using Euler-Lagrange equation for state-based peridynamics. Moreover, application of boundary conditions and determination of surface correction factors are also explained. Finally, the current formulation is verified by considering two benchmark problems including plate under tension and vibration of a plate.

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“…These errors can be corrected by using surface correction factors and modifying the peridynamic dilatation terms and peridynamic force expressions given in Eqs. (8,9,13,14) as…”

Section: Surface Correctionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Derivation of dual-horizon state-based peridynamics formulation based on Euler–Lagrange equation

Wang

Oterkus

Öterkuş

2020

Continuum Mech. Thermodyn.

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“…The PD method evaluates each material particle, making it suitable for dealing with material discontinuity and heterogeneities 1 . Several papers report the PD method's application to simulate various physical problems 5,8–15 …”

Section: Introductionmentioning

confidence: 99%

The fractal version of the bond‐based peridynamics method

Armandei¹,

Sarzosa²,

Savioli³

2021

Numerical Meth Engineering

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This article presents a new formulation of bond‐based peridynamic theory (PD) encompassing material texture heterogeneity through fractal geometry concepts and transforming all relevant variables from Euclidean space to fractal space. The heterogeneity incorporation is realized through the introduction of a linear transformation fractal coefficient (LTFC). By considering a mean value for all LTFCs of all spatial coordinates. For example, x, y, z, and using the relationship between fractal dimension Df and the Hurst exponent H. We present a fractal version of the bond‐based PD method that the equation of motion is conformed to fractal space. Validation of the formulation is accomplished in two steps: first, the effect of irregular mass distribution is characterized by the fractal dimension of the fracture surface roughness through experimental results of a series of single‐edge notched tensile tests of a ductile material. In the next step, the proposed formulation is calibrated with the fractal dimension obtained experimentally. The results are compared with the classical bond‐based PD formulation and the finite element analysis results. The obtained results in this article indicate that the irregular mass distribution of material can be introduced into particle‐based numerical methods using an adequate fractal exponent. The fractal version provides a good approximation of the fracture behavior of materials.

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“…Their results were quite identical to the reference experimental results. Zhu et al [35] extended this BBPD model to ordinary state-based PD (SBPD) which eliminates the restriction of the limitations on material constants due to assumptions of BBPD formulation.…”

Section: Introductionmentioning

confidence: 99%

Thermally-induced fracture analysis of polycrystalline materials by using peridynamics

Lü

Öterkuş

et al. 2020

Engineering Analysis with Boundary Elements

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Polycrystalline materials are widely utilized in engineering fields. In this study, peridynamic (PD) models are developed for the first time in the literature to investigate thermally-induced fracture phenomenon for cubic polycrystals and ceramic made of different materials. After validating the current model, the influences of the grain size, grain boundary strength and composition of the materials on the fracture behavior are analyzed. Two different types of pre-existing cracks, i.e. vertical and horizontal, are considered. The effect of grain size is much more obvious for ceramic materials and crack branching is observed for both vertical and horizontal crack cases. Grain boundary strength has a significant influence on crack behaviour. For weaker grain boundaries intergranular fracture pattern is observed whereas for stronger grain boundaries transgranular crack pattern is more dominant. Crack branching is much more significant when the silicon carbide ratio is higher due to the difference in coefficients of thermal expansion of two different materials. By comparing with the reference results available in the literature similar fracture features are obtained.

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Modelling of Granular Fracture in Polycrystalline Materials Using Ordinary State-Based Peridynamics

Cited by 52 publications

References 45 publications

Derivation of dual-horizon state-based peridynamics formulation based on Euler–Lagrange equation

Derivation of dual-horizon state-based peridynamics formulation based on Euler–Lagrange equation

The fractal version of the bond‐based peridynamics method

Thermally-induced fracture analysis of polycrystalline materials by using peridynamics

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