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Research Papers

Characteristic Volume Element for Randomly Particulate Magnetoactive Composites

[+] Author and Article Information
Alireza Bayat

Composite and Intelligent Materials Laboratory,
Department of Mechanical Engineering,
University of Nevada, Reno,
Reno, NV 89557
e-mail: abayat@unr.edu

Faramarz Gordaninejad

Composite and Intelligent Materials Laboratory,
Department of Mechanical Engineering,
University of Nevada, Reno,
Reno, NV 89557
e-mail: faramarz@unr.edu

1Corresponding author.

Contributed by the Materials Division of ASME for publication in the JOURNAL OF ENGINEERING MATERIALS AND TECHNOLOGY. Manuscript received November 18, 2016; final manuscript received June 1, 2017; published online August 9, 2017. Assoc. Editor: Ghatu Subhash.

J. Eng. Mater. Technol 140(1), 011003 (Aug 09, 2017) (10 pages) Paper No: MATS-16-1336; doi: 10.1115/1.4037023 History: Received November 18, 2016; Revised June 01, 2017

A scale-dependent numerical approach is developed through combining the finite element (FE)-based averaging process with the Monte Carlo method to determine the desired size of a characteristic volume element (CVE) for a random magnetoactive composite (MAC) under applied magnetic field and large deformations. Spatially random distribution of identically magnetic inclusions inside a soft homogeneous matrix is considered to find the appropriate size of the characteristic volume element. Monte Carlo method is used to generate ensembles of a randomly distributed magnetoactive composite to be applied in the homogenization study. The ensemble is utilized as a statistical volume element (SVE) in a scale-dependent numerical algorithm to search the desired characteristic volume element size. Results of this study can be used to investigate effective behavior and multiscale modeling of randomly particulate magnetoactive composites.

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Figures

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Fig. 1

(a) The homogenized body and corresponding boundary decomposition in Lagrangian configuration, (b) corresponding SVE, attached to X¯, selected for statistical analysis including randomly distributed circular permeable particle inside a soft matrix, and (c) the effective medium modeled using homogenization approach

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Fig. 2

Schematic of the statistical algorithm used in the study: (a) selection of random meso-scale ensembles of the heterogeneous MAC for a typical test window size and (b) increasing the size of the test window and number of particles toward the convergence window. All ensembles are generated for Af=0.35,d=10,  and dc=1.

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Fig. 3

Computational algorithm used in the statistical approach

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Fig. 4

Results for normalized modulus component, A, versus number of simulations for (a) LD-BC and (b) PF-BC

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Fig. 5

Results for normalized modulus component, B, versus number of simulations for (a) LD-BC and (b) PF-BC

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Fig. 6

Coefficient of variation of (a) 〈A〉 and (b) 〈B〉 versus scale factor, w

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Fig. 7

Average values of (a) 〈A〉 and (b) 〈B〉 versus scale factor, w

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Fig. 8

FE simulation results for T12 component of microscopic stress tensor for SVEs with (a) w=11, with LD-BC, (b) w=11, with PF-BC, (c) w=13, with LD-BC, and (d) w=13, with PF-BC. All plots are normalized by their average value of T12 component.

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Fig. 9

FE simulation results for B2 component of microscopic magnetic induction vector for SVEs with (a) w=11, with LD-BC, (b) w=11, with PF-BC, (c) w=13, with LD-BC, and (d) w=13, with PF-BC. All plots are normalized by their average value of B2 component.

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Fig. 10

FE simulation results for (a) T12 component of microscopic nominal stress tensor, for converged CVEs, w=27, with LD-BC, (b) B2 component of magnetic induction vector for the converged CVE, w=27 with LD-BC, (c) T12 component of microscopic nominal stress tensor, for converged CVEs with w=25, and PD-BC, and (d) B2 component of magnetic induction vector for the converged CVE, w=25 with PD-BC

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