Investigation of the effect of shape of inclusions on homogenized properties by using peridynamics

Galadima, Yakubu Kasimu; Öterkuş, Erkan; Oterkus, Selda

doi:10.1016/j.prostr.2020.11.124

Cited by 7 publications

(4 citation statements)

References 46 publications

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“…To implement the numerical simulation, the plate was discretised into 10 × 10 grid giving a total of 100 material points. To utilise the recursive function (31) to update the stress at any time t n+1 , a numerical algorithm based on ADR methodology is utilised. This numerical algorithm consists of a two-tier time integration solution strategy.…”

Section: Plate Extensionmentioning

confidence: 99%

“…PD has also been employed to study other nonlocal physical processes such as metal machining process [20], diffusion and other transport phenomena [21][22][23]. Peridynamic frameworks have also been proposed for homogenisation of heterogeneous materials [24][25][26][27][28][29][30][31] as well as multiscale [32][33][34][35][36][37][38] and Multiphysics modelling [39][40][41][42].…”

Section: Introductionmentioning

confidence: 99%

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Modelling of viscoelastic materials using non-ordinary state-based peridynamics

Galadima

Oterkus

Öterkuş

et al. 2023

Engineering with Computers

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This paper proposes a framework for implementing viscoelastic constitutive model from the classical continuum mechanics (CCM) theory within non-ordinary state-based peridynamics (NOSBPD). The motivation stems from the inadequacy of CCM to model very complex material behaviours such as initiation and propagation of cracks and nonlocal behaviour due to size effects. The proposed formulation leverages on the constitutive correspondence between NOSBPD and CCM to incorporate a CCM viscoelastic constitutive model based on hereditary integral into NOSBPD. The combination of hereditary constitutive model and NOSBPD effectively makes this formulation a nonlocal time–space viscoelastic framework where temporal nonlocality is incorporated by a hereditary viscoelastic model which stipulates that the behaviour of a material at any point in time depends on both the present action and the complete history of previous actions on the material, and spatial nonlocality on the other hand is incorporated via the nonlocal mechanism provided by the NOSBPD. For model validation, three benchmark problems were solved using the proposed framework. Results obtained were compared to results from analytical solution and solutions from referenced literature. In addition, parametric study was conducted to determine the influence of nonlocality on numerical prediction. Conclusions drawn from the validation studies presented are that the proposed framework is able to predict viscoelastic responses that agree well with local macro models as well as nonlocal micromodels/nanomodels as reported in the literature.

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Section: Plate Extensionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Modelling of viscoelastic materials using non-ordinary state-based peridynamics

Galadima

Oterkus

Öterkuş

et al. 2023

Engineering with Computers

Self Cite

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“…A family of PD homogenization methods based on strain energy equivalence have been proposed and utilized in [64][65][66][67][68]. The key idea in these methods is that two materials with different microstructure are taken to be constitutively equivalent if the strain energy stored in both materials under affine deformation is the same.…”

Section: Introductionmentioning

confidence: 99%

“…The key idea in these methods is that two materials with different microstructure are taken to be constitutively equivalent if the strain energy stored in both materials under affine deformation is the same. While the method proposed in [67,68] was proposed for application within the BBPD modelling framework, the method proposed in [64] was developed for application in the framework of the ordinary state-based peridynamics and is called ordinary state-based peridynamic homogenization theory (OSBPDHT). It was utilized to study the effective behaviour of elastic materials with evolving microstructure.…”

Section: Introductionmentioning

confidence: 99%

Peridynamic computational homogenization theory for materials with evolving microstructure and damage

Galadima

Xia

Öterkuş

et al. 2022

Engineering with Computers

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This study aims to establish a framework for multiscale assessment of damage for materials with evolving microstructure based on a recently proposed peridynamic computational homogenization theory. The framework starts with replacing a material with complex microstructure with a constitutively equivalent material that is microstructurally homogenous. Constitutive equivalence between the original and the substitute materials is achieved through enforcing strain energy equivalence via the so-called nonlocal Hill’s lemma. The damage law is obtained by numerically solving boundary volume constraint problem of an RVE. The result from the analysis of the RVE problem was compared with the previously published result to establish the validity of the proposed framework. The comparison shows good agreement between result obtained using the proposed framework and those reported in the literature.

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Homogenization of periodic microstructure based on representative volume element using improved bond-based peridynamics

Wang

et al. 2022

Engineering Analysis with Boundary Elements

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Investigation of the effect of shape of inclusions on homogenized properties by using peridynamics

Cited by 7 publications

References 46 publications

Modelling of viscoelastic materials using non-ordinary state-based peridynamics

Modelling of viscoelastic materials using non-ordinary state-based peridynamics

Peridynamic computational homogenization theory for materials with evolving microstructure and damage

Homogenization of periodic microstructure based on representative volume element using improved bond-based peridynamics

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