Boundary Element Method Modelling of Nanocomposites

Ptaszny, J.; Dziatkiewicz, Grzegorz; Fedeliński, P.

doi:10.1615/intjmultcompeng.2014007103

Cited by 7 publications

(4 citation statements)

References 14 publications

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“…In addition to the coexistence of all aggregated, intercalated and exfoliated particles, the number of constitutive nanoclay layers in intercalated and aggregated morphologies vary in different regions of nanoclay reinforced polymer. The majority of studies assumed just either exfoliated or intercalated morphology . Some studies simulated the combination of exfoliated and intercalated ones .…”

Section: Gap Analysismentioning

confidence: 99%

Mechanical Properties of Nanoclay and Nanoclay Reinforced Polymers: A Review

Rafiee

Shahzadi

2018

Polymer Composites

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A literature review is conducted on performed investigations for characterizing Young's modulus of nanoclay platelet as the reinforcing agent of nanoclay/polymer nanocomposites from both experimental and theoretical aspects. The observed discrepancies in the reported results are discussed accordingly. All available investigations for predicting mechanical properties of nanoclay reinforced polymers are also reviewed. The employed methods in ongoing studies are categorized into three groups as atomistic, continuum and multiscale modeling techniques. Those challenging issues which are still in need of more accurate understanding and discussion are identified and outlined through a gap analysis on current investigations. The introduced shortcomings can be considered as prospective research areas for the future studies in the field of estimating mechanical properties of nanoclay based composites. POLYM. COMPOS., 40:431–445, 2019. © 2018 Society of Plastics Engineers

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Section: Gap Analysismentioning

confidence: 99%

Mechanical Properties of Nanoclay and Nanoclay Reinforced Polymers: A Review

Rafiee

Shahzadi

2018

Polymer Composites

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“…The BEM was successfully applied in the analysis of 2D and 3D nonhomogeneous materials containing pores, by Hu et al (2000), Liu (2009), Ptaszny and Fedeliński (2007), Fedeliński et al (2014), Ptaszny et al (2014), Ptaszny and Fedeliński (2011a), Rejwer et al (2014) and Ptaszny (2015), cracks, by Yoshida et al (2001), Liu (2009), Fedeliński et al (2014), Rejwer et al (2014) and Trinh et al (2015) and composite materials, by Kamiński (1999), Liu et al (2005), Chen and Liu (2005), Lei et al (2006), Liu (2009), Ptaszny and Fedeliński (2011b), Fedeliński et al (2014) and Huang et al (2015). However, as far as we know, there is a lack of comprehensive comparison between the higher-order approximation BEM and FEM in 3D large-scale analysis in the literature.…”

Section: Introductionmentioning

confidence: 99%

Evaluation of the FMBEM efficiency in the analysis of porous structures

Ptaszny

Hatłas²

2018

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Purpose The purpose of this paper is to evaluate the efficiency of the fast multipole boundary element method (FMBEM) in the analysis of stress and effective properties of 3D linear elastic structures with cavities. In particular, a comparison between the FMBEM and the finite element method (FEM) is performed in terms of accuracy, model size and computation time. Design/methodology/approach The developed FMBEM uses eight-node Serendipity boundary elements with numerical integration based on the adaptive subdivision of elements. Multipole and local expansions and translations involve solid harmonics. The proposed model is used to analyse a solid body with two interacting spherical cavities, and to predict the homogenized response of a porous material under linear displacement boundary condition. The FEM results are generated in commercial codes Ansys and MSC Patran/Nastran, and the results are compared in terms of accuracy, model size and execution time. Analytical solutions available in the literature are also considered. Findings FMBEM and FEM approximate the geometry with similar accuracy and provide similar results. However, FMBEM requires a model size that is smaller by an order of magnitude in terms of the number of degrees of freedom. The problems under consideration can be solved by using FMBEM within the time comparable to the FEM with an iterative solver. Research limitations/implications The present results are limited to linear elasticity. Originality/value This work is a step towards a comprehensive efficiency evaluation of the FMBEM applied to selected problems of micromechanics, by comparison with the commercial FEM codes.

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“…[6,8,[24][25][26][27][28]) and 3D microstructures (e.g. [3,10,14,17,19,32,35]), containing pores, cracks, particles and fibers.…”

Section: Introductionmentioning

confidence: 99%

“…(24),(25) in the Appendix). Terms of the expansions are products of multipole functions and moments.…”

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confidence: 99%

Accuracy of the fast multipole boundary element method with quadratic elements in the analysis of 3D porous structures

Ptaszny

2015

Comput Mech

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In this work, a fast multipole boundary element method for 3D elasticity problem was developed by the application of the fast multipole algorithm and isoparametric 8-node boundary elements with quadratic shape functions. The problem is described by the boundary integral equation involving the Kelvin solutions. In order to keep the numerical integration error on appropriate level, an adaptive method with subdivision of boundary elements into subelements, described in the literature, was applied. An extension of the neighbour list of boundary element clusters, corresponding to near-field computations, was proposed in order to reduce the truncation error of expansions in problems with high stress concentration. Efficiency of the method is illustrated by numerical examples including a solid with single spherical cavity, solids with two interacting spherical cavities, and numerical homogenization of solids with cubic arrangement of spherical cavities. All results agree with analytical models available in the literature. The examples show that the method can be applied to the analysis of porous structures.

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Boundary Element Method Modelling of Nanocomposites

Cited by 7 publications

References 14 publications

Mechanical Properties of Nanoclay and Nanoclay Reinforced Polymers: A Review

Mechanical Properties of Nanoclay and Nanoclay Reinforced Polymers: A Review

Evaluation of the FMBEM efficiency in the analysis of porous structures

Accuracy of the fast multipole boundary element method with quadratic elements in the analysis of 3D porous structures

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