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Research Papers

A Simple Transversely Isotropic Hyperelastic Constitutive Model Suitable for Finite Element Analysis of Fiber Reinforced Elastomers

[+] Author and Article Information
Leslee W. Brown

 Gates Corporation, 2975 Waterview Drive, Rochester Hills, MI 48309lwbrown@aol.com

Lorenzo M. Smith

Department of Mechanical Engineering, Oakland University, 118 Dodge Hall, Rochester, MI 48309l8smith@oakland.edu

J. Eng. Mater. Technol 133(2), 021021 (Mar 23, 2011) (13 pages) doi:10.1115/1.4003517 History: Received May 26, 2010; Revised December 31, 2010; Published March 23, 2011; Online March 23, 2011

A transversely isotropic fiber reinforced elastomer’s hyperelasticity is characterized using a series of constitutive tests (uniaxial tension, uniaxial compression, simple shear, and constrained compression test). A suitable transversely isotropic hyperelastic invariant based strain energy function is proposed and methods for determining the material coefficients are shown. This material model is implemented in a finite element analysis by creating a user subroutine for a commercial finite element code and then used to analyze the material tests. A useful set of constitutive material data for multiple modes of deformation is given. The proposed strain energy function fits the experimental data reasonably well over the strain region of interest. Finite element analysis of the material tests reveals further insight into the materials constitutive nature. The proposed strain energy function is suitable for finite element use by the practicing engineer for small to moderate strains. The necessary material coefficients can be determined from a few simple laboratory tests.

Copyright © 2011 by American Society of Mechanical Engineers
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References

Figures

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Tensile test results

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Tensile anisotropy

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Compression test

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Compression test results

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Compression anisotropy

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Dual lap shear test

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Dual lap shear test results

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Constrained volume compression test results

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Comparison of models and measured results for WG uniaxial stress

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Finite element model of short fiber

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Comparison of reinforcing functions with predicted results for short fiber

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Uniaxial deformation

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Simple shear deformation

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Pure shear (plane strain) deformation

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Minimized difference material model fit

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Deterministic material model fit

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Tensile test finite element model

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Tensile FEA second PK stress contours (MPa)

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Tensile FEA results

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Distributed fiber orientation finite element model

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Distributed fiber FEA results

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Compression finite element model

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Compression FEA results

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V Compression FEA second PK stress contours (MPa)

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H Compression FEA second PK stress contours (MPa) and laminated structure

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XG Compression second PK stress contours (MPa)

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Simple shear finite element model

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Simple shear FEA results

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Simple shear FEA second PK stress contours (MPa)

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Simple Shear FEA internal second PK stress contours (MPa)

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