Editorial Type:
Article Category: Research Article
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Online Publication Date: 01 Dec 2009

A Three-Dimensional Constitutive Model for the Dynamic Response of Rubber3

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Page Range: 226 – 253
DOI: 10.2346/1.3148303
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Abstract

REFERENCE: Liu, M. and Hoo Fatt, M. S., "A Three-Dimensional Constitutive Model for the Dynamic Response of Rubber," Tire Science and Technology, TSTCA, Vol. 37, No. 4, October - December 2009, pp. 226-253.

The development of a constitutive model to describe the dynamic response of a filled rubber compound is presented in this paper. A series of cyclic tension tests were done on the rubber compound with mean strains ranging from 0.2 to 0.5, strain amplitudes ranging from 0.05 to 0.2, and strain rates ranging from 0.1 to 10 s−1. The cyclic strain-controlled test results showed material rate dependence and hysteresis, and this motivated the development of a phenomenological-based, hyper-viscoelastic constitutive model. A Zener model, i.e., a spring in parallel with a Maxwell element, was assumed. The total stress was decomposed into a rate-independent equilibrium stress and a rate-dependent overstress. The springs were modeled as neo-Hookean, while the damper was defined by a nonlinear viscosity function. Material constants for the constitutive model were calculated from the cyclic tension test results. Cyclic tension tests were also performed on a sheet with central hole to check the accuracy of the constitutive model. The constitutive model was implemented into ABAQUS Standard with a user-defined material subroutine. The finite element analysis simulation of the rubber sheet with a central hole demonstrated relatively good agreement with the experimental data.

Keywords: dynamic constitutive model; FEA; rubber
Copyright: The Tire Society
FIG. 1.
FIG. 1.

Geometry of uniaxial tensile specimen: (a) strip specimen and (b) hole-in-sheet specimen.

FIG. 2.
FIG. 2.

Preconditioning: (a) five-cycle hysteresis and (b) cyclic strain history for a 10 s−1 test.

FIG. 3.
FIG. 3.

Hysteresis curves at mean strain of 0.3 and strain rate of 1 s−1 (varying strain amplitude).

FIG. 4.
FIG. 4.

Steady-state hysteresis curves at strain rate of 1 s−1 and strain amplitude of 0.2 (varying mean strain).

FIG. 5.
FIG. 5.

Strain history of the step relaxation test.

FIG. 6.
FIG. 6.

Cauchy stress strain from step relaxation test.

FIG. 7.
FIG. 7.

Master hysteresis curves showing effect of strain rate.

FIG. 8.
FIG. 8.

Comparison of FEA results with the experimental data: (a) stable hysteresis for sheet with 9.525-mm-diameter hole at different strain rates and (b) stable hysteresis at strain rate of 1 s−1 for sheets with different diameters.

FIG. 9.
FIG. 9.

A Zener model.

FIG. 10.
FIG. 10.

Multiplicative decomposition.

FIG. 11.
FIG. 11.

Equilibrium, overstress, and master curves.

FIG. 12.
FIG. 12.

Viscosity function for mean strain of 0.3, strain amplitude of 0.2, and strain rate of 1 s−1.

FIG. 13.
FIG. 13.

Finite element half-model of the hole-in-the-sheet.

FIG. 14.
FIG. 14.

Comparison of FEA results with the experimental data: (a) force history for sheet with 9.525-mm-diameter hole at different strain rates. (b) Force history at strain rate of 1 s−1 for sheets with different diameters.

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