Peridynamic Modelling of Fracture in Polycrystalline Ice

Lü, Wei; Li, Mingyang; Važić, Božo; Oterkus, Selda; Öterkuş, Erkan; Wang, Qing

doi:10.1017/jmech.2019.61

Cited by 26 publications

(9 citation statements)

References 30 publications

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“…Note that in Eqs. (10) and (11), the micropotential being zero means one of the material points is not within the horizon of the other material point. As shown in Fig.…”

Section: Dual-horizon Peridynamics Formulation Based On Euler-lagrangmentioning

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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“…Note that in Eqs. (10) and (11), the micropotential being zero means one of the material points is not within the horizon of the other material point. As shown in Fig.…”

Section: Dual-horizon Peridynamics Formulation Based On Euler-lagrangmentioning

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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“…PD has been extensively applied to simulate crack growth in a wide range of materials and structures under different loading conditions [12][13][14][15][16][17][18][19][20][21][22][23][24][25]. A limited number of PD formulations for FSI phenomena may be found in the literature, e.g., hydraulic fracturing [26][27][28], ice-water interaction [29], ice-structure interaction [30,31], and fluidelastic structure interaction [32,33]. In our proposed FSI methodology, a stable correspondence-based PD formulation [34] is utilized, which enables direct use of classical continuum material and damage models.…”

Section: Introductionmentioning

confidence: 99%

Coupling of IGA and Peridynamics for Air-Blast Fluid-Structure Interaction Using an Immersed Approach

Behzadinasab

Moutsanidis

Trask

et al. 2021

Preprint

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We present a novel formulation based on an immersed coupling of Isogeometric Analysis (IGA) and Peridynamics (PD) for the simulation of fluid-structure interaction (FSI) phenomena for air blast. We aim to develop a practical computational framework that is capable of capturing the mechanics of air blast coupled to solids and structures that undergo large, inelastic deformations with extreme damage and fragmentation. An immersed technique is used, which involves an a priori monolithic FSI formulation with the implicit detection of the fluid-structure interface and without limitations on the solid domain motion. The coupled weak forms of the fluid and structural mechanics equations are solved on the background mesh. Correspondence-based PD is used to model the meshfree solid in the foreground domain. We employ the Non-Uniform Rational B-Splines (NURBS) IGA functions in the background and the Reproducing Kernel Particle Method (RKPM) functions for the PD solid in the foreground. We feel that the combination of these numerical tools is particularly attractive for the problem class of interest due to the higher-order accuracy and smoothness of IGA and RKPM, the benefits of using immersed methodology in handling the fluid-structure coupling, and the capabilities of PD in simulating fracture and fragmentation scenarios. Numerical examples are provided to illustrate the performance of the proposed air-blast FSI framework.

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“…Liu et al [39] coupled PD with updated Lagrangian particle hydrodynamics to simulate icewater interactions. The PD theory is also used for ice modelling by including the ice breakage 4 [40][41][42]. The updated Lagrangian particle hydrodynamics (ULPH) proposed by Tu et al [43] is utilized to simulate the fluid flow.…”

Section: Introductionmentioning

confidence: 99%

Fluid-elastic structure interaction simulation by using ordinary state-based peridynamics and peridynamic differential operator

Gao

Oterkus

2020

Engineering Analysis with Boundary Elements

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The fluid-structure interaction phenomenon is often encountered in the ocean engineering field.In the present work, a non-local numerical model is developed for the simulations of weakly compressible viscous fluid and elastic structure interactions. The peridynamic theory is adopted for both the structure and fluid modelling. The elastic structure is described by using the ordinary state-based peridynamics, while the fluid is modelled by utilizing the peridynamic differential operator. Furthermore, the updated Lagrangian description is adopted for the fluid including the relative deformation gradient expressed by the peridynamic differential operator.The fluid-structure interface and its normal direction are calculated via the gradient of a colour function, which varies with the fluid motion and structure deformation. Besides, the interaction force exerted from fluid to structure is constrained to be always perpendicular to the moving interface. Hence the fluid motion and structural deformation are predicted simultaneously. The validation of the developed model is conducted through the simulation of a water dam break with a rubber gate. The good agreement between the peridynamic and the experiment results demonstrates the capability of the current model for solving fluid-elastic structure interaction problems.

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Peridynamic Modelling of Fracture in Polycrystalline Ice

Cited by 26 publications

References 30 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

Coupling of IGA and Peridynamics for Air-Blast Fluid-Structure Interaction Using an Immersed Approach

Fluid-elastic structure interaction simulation by using ordinary state-based peridynamics and peridynamic differential operator

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