Mixed Finite Element Analysis of Elastomeric Butt-Joints

[+] Author and Article Information
P. A. Kakavas

 Technological Educational Institute of Patras, 1 M. Alexandrou Street, GR-26334 Patras, Greecekakavas@teipat.gr

G. I. Giannopoulos, N. K. Anifantis

Machine Design Laboratory, Mechanical and Aeronautics Engineering Department,  University of Patras, GR-26500 Patras, Greece

J. Eng. Mater. Technol 129(1), 11-18 (Sep 27, 2005) (8 pages) doi:10.1115/1.2400254 History: Received August 02, 2003; Revised September 27, 2005

This paper presents a mixed finite element formulation approximating large deformations observed in the analysis of elastomeric butt-joints. The rubber has been considered as nearly incompressible continuum obeying the Mooney/Rivlin (M/R) strain energy density function. The parameters of the model were determined by fitting the available from the literature uniaxial tension experimental data with the constitutive equation derived from the M/R model. The optimum value of the Poisson ratio is adjusted by comparing the experimentally observed diametral contraction of the model with that numerically obtained using the finite element method. The solution of the problem has been obtained utilizing the mixed finite element procedure on the basis of displacement/pressure mixed interpolation and enhanced strain energy mixed formulation. For comparison purposes, an axisymmetric with two-parameter M/R model and a three-dimensional (3D) with nine-parameters M/R model of the butt-joint are formulated and numerical results are illustrated concerning axisymmetric or general loading. For small strains the stress and/or strain distribution in the 2D axisymmetric butt-joint problem was compared with derived analytical solutions. Stress distributions along critical paths are evaluated and discussed.

Copyright © 2007 by American Society of Mechanical Engineers
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Figure 1

Sketch of an elastomeric butt-joint specimen with its geometrical characteristics

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Figure 2

Fitting of experimental stress–stretch curve of the filled SBR rubber using M/R strain energy function with two and nine terms

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Figure 3

Prediction of appropriate Poisson ratio value through comparisons of FEM solutions with experimental results of the diametrical contraction corresponding to tensional deformation

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Figure 4

Numerical prediction of the axial, shear, and radial stress distribution in a butt-joint specimen using the FEM analysis and comparison with analytical solution

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Figure 5

Distribution stress components along the free surface of the butt-joint specimen

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Figure 6

Axial stress distribution along the steel/rubber interface for various values of the applied strain

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Figure 7

Deformed mesh of the 3D FEM model of the butt joint in xz plane corresponding to: (a) tension, (b) compression, (c) bending, and (d) pure shear loading conditions

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Figure 8

Stresses in tension and compression as a function of normalized distance

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Figure 9

Stresses in bending as a function of normalized distance: (a) along the x axis; and (b) along the y axis

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Figure 10

Stresses in shear as a function of normalized distance: (a) along the x axis; and (b) along the y axis



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