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Research Papers

A Nonlinear Rubber Material Model Combining Fractional Order Viscoelasticity and Amplitude Dependent Effects

[+] Author and Article Information
N. Gil-Negrete1

Department of Applied Mechanics, CEIT and Tecnun (University of Navarra), Paseo Manuel Lardizabal 15, 20018 San Sebastian, Spainngil@ceit.es

J. Vinolas

Department of Applied Mechanics, CEIT and Tecnun (University of Navarra), Paseo Manuel Lardizabal 15, 20018 San Sebastian, Spain

L. Kari

Department Aeronautical and Vehicle Engineering, MWL, KTH, SE-10044 Stockholm, Sweden

1

Corresponding author.

J. Appl. Mech 76(1), 011009 (Nov 05, 2008) (9 pages) doi:10.1115/1.2999454 History: Received February 18, 2008; Revised July 16, 2008; Published November 05, 2008

A nonlinear rubber material model is presented, where influences of frequency and dynamic amplitude are taken into account through fractional order viscoelasticity and plasticity, respectively. The problem of simultaneously modeling elastic, viscoelastic, and friction contributions is removed by additively splitting them. Due to the fractional order representation mainly, the number of parameters of the model remains low, rendering an easy fitting of the values from tests on material samples. The proposed model is implemented in a general-purpose finite element (FE) code. Since commercial FE codes do not contain any suitable constitutive model that represents the full dynamic behavior of rubber compounds (including frequency and amplitude dependent effects), a simple approach is used based on the idea of adding stress contributions from simple constitutive models: a mesh overlay technique, whose basic idea is to create a different FE model for each material definition (fractional derivative viscoelastic and elastoplastic), all with identical meshes but with different material definition, and sharing the same nodes. Fractional-derivative viscoelasticity is implemented through user routines and the algorithm for that purpose is described, while available von Mises’ elastoplastic models are adopted to take rate-independent effects into account. Satisfactory results are obtained when comparing the model results with tests carried out in two rubber bushings at a frequency range up to 500 Hz, showing the ability of the material model to accurately describe the complex dynamic behavior of carbon-black filled rubber compounds.

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Copyright © 2009 by American Society of Mechanical Engineers
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References

Figures

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Figure 11

Axial stiffness of bushing 1. T: experimental test; N: simulation in the FE code.

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Figure 12

Complex dynamic stiffness of bushing 1 in the softest radial direction. T: experimental test; N: simulation in the FE code.

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Figure 13

Axial stiffness of bushing 2. T: Experimental test; N: Simulation in the FE code.

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Figure 14

Radial stiffness of bushing 2. T: Experimental test; N: Simulation in the FE code.

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Figure 1

Simple shear specimen

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Figure 2

Magnitude of shear modulus (MPa) as a function of frequency. Dynamic strain amplitude of 0.02 mm. Room temperature (23°C).

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Figure 3

Magnitude of shear modulus (MPa) as a function of dynamic strain amplitude. Frequency of 102 Hz. Room temperature (23°C).

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Figure 4

Loss angle of shear modulus (deg) as a function of dynamic strain amplitude. Frequency of 102 Hz. Room temperature (23°C).

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Figure 5

Mechanical analogy of the non-linear material model adopted

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Figure 6

Frequency dependent complex shear modulus provided by fractional order Zener modulus for different values of α

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Figure 7

Rate-independent behavior of a unique Maxwell friction chain

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Figure 8

Practical procedure to obtain the dynamic stiffness of components

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Figure 9

Bushing 1: cylindrical rubber bushing with two holes. Shore A 50.

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Figure 10

Bushing 2: cylindrical rubber bushing. Shore A 70.

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