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An analytical study on prediction of effective elastic constants of perforated plate

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Abstract

In this study, the validity of the Eshelby-type model for predicting the effective Young’s modulus and in-plane Poisson’s ratio of the 2-dimensional perforated plate has been investigated in terms of the porosity size and its arrangement. The predicted results by the Eshelbytype model are compared with those by finite element analysis. Whenever the ratio of the porosity size to the specimen size becomes smaller than 0.07, the effective elastic constants predicted by finite element analysis are convergent regardless of the arrangement of the porosities. Under these conditions, the effective Young’s moduli of the perforated plate can be predicted within the accuracy of 5% by the Eshelby-type model, which overestimates and underestimates the effective Poisson’s ratios by 10% and 6% for the plates with periodically and non-periodically arranged porosities, respectively.

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Abbreviations

λ :

Lame’s constant

μ :

Lame’s constant

ν :

Poisson’s ratio

σℴ :

Applied stress

Ω :

Porosities domain

D=Ω :

Solid domain

C :

Stiffness

d :

Diameter of the porosity

E :

Young’s modulus of the solid

e° :

Strain field induced in the solid without porosities by σ°

ē :

Average disturbance of the strain field in the solid

e :

Disturbed strain field in the porosities

e* :

Eigenstrain field of Eshelby’s equivalent inclusion method

ec :

Total strain field of the perforated plate

em :

Total strain field in the solid

ep :

Total strain field in the porosities

f :

Volume fraction of porosities

L :

Length of the perforated plate

N :

Number of the porosities

S :

Eshelby tensor

W :

Width of the perforated plate

c :

The perforated plate

m :

Solid

p :

Porosities

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Authors and Affiliations

  1. School of Mechanical and Automotive Engineering, Catholic University of Daegu, 712-702, Gyeongsansi, Gyeongbuk, Korea

    Jae-Kon Lee & Jin-Gon Kim

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  1. Jae-Kon Lee
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  2. Jin-Gon Kim
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Correspondence to Jin-Gon Kim.

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Lee, JK., Kim, JG. An analytical study on prediction of effective elastic constants of perforated plate. J Mech Sci Technol 19, 2224–2230 (2005). https://doi.org/10.1007/BF02916462

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  • DOI: https://doi.org/10.1007/BF02916462

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