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MULTI-PHYSICS APPROACHES FOR THE BEHAVIOR OF POLYMER-BASED MATERIALS

Modeling of the Stress–Birefringence–Stretch Behavior in Rubbers Using the Gent Model

[+] Author and Article Information
A. K. Mossi Idrissa, Y. Rémond

 University of Strasbourg, IMFS, CNRS, 2 Rue Boussingault, 67000 Strasbourg, France

S. Ahzi1

 University of Strasbourg, IMFS, CNRS, 2 Rue Boussingault, 67000 Strasbourg, France;  University of Aveiro, TEMA, 3810-193 Aveiro, Portugal e-mail: ahzi@unistra.fr

J. Gracio

 University of Aveiro, TEMA, 3810-193 Aveiro, Portugal

1

Corresponding author.

J. Eng. Mater. Technol 133(3), 030905 (Jul 01, 2011) (8 pages) doi:10.1115/1.4004053 History: Received July 16, 2010; Revised April 01, 2011; Published July 01, 2011

In this paper, we discuss the application of different stress–optic laws for rubbers to predict the birefringence evolution and the stress–stretch relationship. The main focus of this work is to propose a new formulation for the stress–birefringence relationship using the Gent theory for rubber elasticity. The Gent constitutive model for the stress–stretch response has been shown to provide a nearly equivalent rubber elastic behavior as that of the widely used eight-chain model. By combining the simpler stress–stretch relationship from the Gent model with a Gaussian network theory for birefringence, we propose a simplified stress–optic relationship. We show that our obtained results are in accord with the existing experimental results at large strains. Our proposed simplified formulation and results allow us to conclude that the Gent theory can be extended to predict optical anisotropy evolution under large strains and that these predictions are nearly equivalent to the more complex formulation based on the eight-chain model.

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Copyright © 2011 by American Society of Mechanical Engineers
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Figures

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Figure 1

PDMS(A) stress–stretch (a) and birefringence–stretch (b) responses under uniaxial tension (Δη1-2=Δη1-3)

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Figure 2

PDMS(B) stress–stretch (a) and birefringence–stretch (b) responses under uniaxial tension (Δη1-2=Δη1-3)

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Figure 3

PDMS(C) stress–stretch (a) and birefringence–stretch (b) responses under uniaxial compression (Δη1-2=Δη1-3)

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Figure 4

PDMS(D) stress–stretch (a) and birefringence–stretch (b) responses under uniaxial compression (Δη1-2=Δη1-3)

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Figure 5

Natural rubber stress–stretch (a) and birefringence–stretch (b) responses under uniaxial tension (Δη1-2=Δη1-3)

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Figure 6

The difference between expressions A and B for N=10.89 or Jm=29.67

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Figure 7

The difference between expressions A and B for N=50 or Jm=147

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