Fully coupled poroelastic peridynamic formulation for fluid-filled fractures

Oterkus, Selda; Madenci, Erdogan; Öterkuş, Erkan

doi:10.1016/j.enggeo.2017.02.001

Cited by 103 publications

(46 citation statements)

References 37 publications

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“…PD-FEM coupling is an approach aimed at taking advantage of both methods [79][80][81][82]. The interest in PD can also be understood from the coupling of PD with other formulations such as classical elasticity [83], poroelasticity [41,84], MD [85,86], finite point method [87] as well as damage models [88].…”

Section: General Coupling Techniquesmentioning

confidence: 99%

Peridynamics review

Javili

Morasata

Öterkuş

et al. 2018

Mathematics and Mechanics of Solids

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223

109

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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: General Coupling Techniquesmentioning

confidence: 99%

Peridynamics review

Javili

Morasata

Öterkuş

et al. 2018

Mathematics and Mechanics of Solids

Self Cite

223

109

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“…al. 2008), porous flow (Oterkus et al, 2017), etc. PD theory has also been effectively used for impact analysis (Amani et al, 2016).…”

Section: Introductionmentioning

confidence: 99%

A Kirchhoff plate formulation in a state-based peridynamic framework

Yang¹,

Važić

Diyaroglu

et al. 2019

Mathematics and Mechanics of Solids

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In recent years, there has been rapid progress on peridynamics. It has been applied to many different material systems, used for coupled field analysis and is suitable for multi-scale analysis. This study mainly focuses on peridynamic analysis for plate-type structures. For this purpose, a new peridynamic Kirchhoff plate is developed. The new formulation is computationally efficient by having only one degree of freedom for each material point. Moreover, it is based on the state-based peridynamic formulation, which does not impose any limitation on material constants. After presenting how to impose simply supported and clamped boundary conditions in this new formulation, several numerical studies are considered to demonstrate the accuracy and capability of the proposed formulation.

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“…They utilized a cumulative damage concept to track the broken mechanical bonds for each material point. Oterkus et al [55] formulated a fully coupled poroelastic framework for fluid flow in fracturing porous media using bond-based peridynamics in which Poisson's ratio is limited to one quarter. Jabakhanji and Mohtar [56] presented a bond-based peridynamic model for unsaturated fluid flow in soils.…”

Section: Introductionmentioning

confidence: 99%

Coupled Analysis of Desiccation Cracking in Unsaturated Soils through a Non-Local Mathematical Formulation

Menon

Song

2019

Geosciences

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The formation of desiccation cracks in unsaturated soils as a discontinuity phenomenon can compromise the integrity of civil infrastructure on unsaturated soils. Because of the singularity at such discontinuities, the mathematical modeling of desiccation cracking is challenging. In this study, we apply a coupled nonlocal peridynamic poroelastic framework to model desiccation cracking in unsaturated soils. The soil skeleton is modeled by a nonlocal peridynamic elastic solid. A peridynamic equivalence of the generalized Darcy’s law is utilized to model unsaturated fluid flow. Cracking is determined by a critical stretch criterion between material points as well as an energy criterion. We present numerical simulations of desiccation cracking in soil bars and thin soil discs for one-dimensional cracking and two-dimensional cracking networks, respectively. The numerical results have demonstrated that the proposed nonlocal mathematical framework is a promising and robust method for modeling desiccation cracking in unsaturated soils.

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Fully coupled poroelastic peridynamic formulation for fluid-filled fractures

Cited by 103 publications

References 37 publications

Peridynamics review

Peridynamics review

A Kirchhoff plate formulation in a state-based peridynamic framework

Coupled Analysis of Desiccation Cracking in Unsaturated Soils through a Non-Local Mathematical Formulation

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