Numerical homogenization by using the fast multipole boundary element method

Ptaszny, J.; Fedelińnaski, P.

doi:10.1016/s1644-9665(12)60182-4

Cited by 10 publications

(4 citation statements)

References 13 publications

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“…The aim of the numerical homogenization is to determine continuous, effective coefficients of differential equations which are applied to a higher scale. A typical attitude in the numerical homogenization consists in the determination of constitutive relation between averaged field variables, like stresses and strains (Ptaszny and Fedeliński, 2011). …”

Section: Multiscale Modellingmentioning

confidence: 99%

Multiobjective and multiscale optimization of composite materials by means of evolutionary computations

Beluch

Długosz

2016

jtam

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The paper deals with the multiobjective and multiscale optimization of heterogeneous structures by means of computational intelligence methods. The aim of the paper is to find optimal properties of composite structures in a macro scale modifying their microstructure. At least two contradictory optimization criteria are considered simultaneously. A numerical homogenization concept with a representative volume element is applied to obtain equivalent macro-scale elastic constants. An in-house multiobjective evolutionary algorithm MOOP-TIM is applied to solve the considered optimization tasks. The finite element method is used to solve the boundary-value problem in both scales. A numerical example is attached.

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Section: Multiscale Modellingmentioning

confidence: 99%

Multiobjective and multiscale optimization of composite materials by means of evolutionary computations

Beluch

Długosz

2016

jtam

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“…Advanced nanocomposites filled by nanoscale particles have attracted much attention from scientists and engineers. [1][2][3][4][5] These nanocomposites have numerous applications in a wide range of temperature sensing elements, actuators, aerospace industry, biological micro-electro-mechanical devices etc. [6][7][8][9][10] Among them, the carbon nanotube (CNT)-reinforced polymer nanocomposite is one of the most popular materials indicating excellent mechanical, thermal and electrical properties at a low level of CNTs.…”

Section: Introductionmentioning

confidence: 99%

Multi-axial elastic–viscoplastic curves of unidirectional carbon nanotube-polymer nanocomposites considering interphase and interface debonding using finite element modeling

Ahmadi

Ansari

Hassanzadeh-Aghdam

2023

Journal of Composite Materials

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This paper aims to predict the elastic-viscoplastic curves of unidirectional carbon nanotube (CNT)-reinforced polymer nanocomposites under the multi-axial tensions, including bi-axial transverse-transverse, bi-axial longitudinal-transverse and tri-axial longitudinal-transverse-transverse loadings by the use of finite element (FE) modeling. The role of the interphase between the CNT and polymer matrix as well as the debonding at the CNT/interphase interface in the stress-strain curves of nanocomposites is investigated. The polymer matrix and interphase region are characterized as elastic-viscoplastic materials, while the CNT behaves as the elastic material. The present results in uni-axial loading are compared to the available numerical outcomes for indicating the accuracy of the FE modeling. The simulation of multi-axial load conditions is based on the three-dimensional representative volume element (RVE) of the unidirectional CNT-polymer nanocomposite. The effect of interface strength on the elastic-viscoplastic stress-strain curves is examined under bi-axial and tri-axial loadings.

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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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Numerical homogenization by using the fast multipole boundary element method

Cited by 10 publications

References 13 publications

Multiobjective and multiscale optimization of composite materials by means of evolutionary computations

Multiobjective and multiscale optimization of composite materials by means of evolutionary computations

Multi-axial elastic–viscoplastic curves of unidirectional carbon nanotube-polymer nanocomposites considering interphase and interface debonding using finite element modeling

Evaluation of the FMBEM efficiency in the analysis of porous structures

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