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Research Papers

The Exponentiated Hencky Strain Energy in Modeling Tire Derived Material for Moderately Large Deformations

[+] Author and Article Information
Giuseppe Montella

Department of Structure for Engineering
and Architecture,
University of Naples ‘Federico II’,
Naples 80125, Italy;
Department of Civil
and Environmental Engineering,
University of California Berkeley,
Berkeley, CA 94720
e-mail: giuseppe.montella@unina.it

Sanjay Govindjee

Professor
Mem. ASME
Department of Civil
and Environmental Engineering,
University of California Berkeley,
Berkeley, CA 94720
e-mail: s_g@berkeley.edu

Patrizio Neff

Professor
Faculty of Mathematics,
University of Duisburg-Essen,
Essen 45117, Germany
e-mail: patrizio.neff@uni-due.de

Contributed by the Materials Division of ASME for publication in the JOURNAL OF ENGINEERING MATERIALS AND TECHNOLOGY. Manuscript received September 17, 2015; final manuscript received January 19, 2016; published online May 10, 2016. Assoc. Editor: Curt Bronkhorst.

J. Eng. Mater. Technol 138(3), 031008 (May 10, 2016) (12 pages) Paper No: MATS-15-1232; doi: 10.1115/1.4032749 History: Received September 17, 2015; Revised January 19, 2016

This work presents a hyperviscoelastic model, based on the Hencky-logarithmic strain tensor, to model the response of a tire derived material (TDM) undergoing moderately large deformations. The TDM is a composite made by cold forging a mix of rubber fibers and grains, obtained by grinding scrap tires, and polyurethane binder. The mechanical properties are highly influenced by the presence of voids associated with the granular composition and low tensile strength due to the weak connection at the grain–matrix interface. For these reasons, TDM use is restricted to applications involving a limited range of deformations. Experimental tests show that a central feature of the response is connected to highly nonlinear behavior of the material under volumetric deformation which conventional hyperelastic models fail in predicting. The strain energy function presented here is a variant of the exponentiated Hencky strain energy, which for moderate strains is as good as the quadratic Hencky model and in the large strain region improves several important features from a mathematical point of view. The proposed form of the exponentiated Hencky energy possesses a set of parameters uniquely determined in the infinitesimal strain regime and an orthogonal set of parameters to determine the nonlinear response. The hyperelastic model is additionally incorporated in a finite deformation viscoelasticity framework that accounts for the two main dissipation mechanisms in TDMs, one at the microscale level and one at the macroscale level. The new model is capable of predicting different deformation modes in a certain range of frequency and amplitude with a unique set of parameters with most of them having a clear physical meaning. This translates into an important advantage with respect to overcoming the difficulties related to finding a unique set of optimal material parameters as are usually encountered fitting the polynomial forms of strain energies. Moreover, by comparing the predictions from the proposed constitutive model with experimental data we conclude that the new constitutive model gives accurate prediction.

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References

Figures

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Fig. 1

TDM: (a) TDM pad and (b) close up view

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Fig. 2

Comparison between shear stress corresponding to exponentiated Hencky energy WeHm, Eq. (9), and experimental tests for different densities: (a) TDM 500, (b) TDM 600, and (c) TDM 800

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Fig. 3

Compression test procedure. First figure (a) shows strain history. In (b)-(d), the lower (blue) curve represents the true data and the upper (red) curve represents the assumed equilibrium response from the data: (a) strain history, (b) TDM 500, (c) TDM 600, and (d) TDM 800.

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Fig. 4

Original image from the digital camera (left column) versus image after processing (right column) for TDM 600 at 0%, 35%, and 70% deformation

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Fig. 5

Nonlinear Poisson's coefficient ν̂ evaluated during compression tests

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Fig. 6

Comparison between compression stress corresponding to modified exponentiated Hencky energy WeHm, Eqs. (15) and (16), and experimental tests for different densities (a) TDM 500, (b) TDM 600, and (c) TDM 800

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Fig. 7

Comparison between pseudovolumetric response corresponding to Eq. (6) and experimental tests for different densities with p≈σ11 (a) TDM 500, (b) TDM 600, and (c) TDM 800

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Fig. 8

One-dimensional rheological model for rate-dependent behavior of TDM

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Fig. 9

Comparison between cyclic shear tests (markers) and the viscoelastic model based on the modified exponentiated Hencky energy WeHmv (solid line), Eq. (19), for different frequencies at 100% amplitude: (a) TDM 500, (b) TDM 600, and (c) TDM 800

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Fig. 10

Comparison between cyclic shear tests (markers) and the viscoelastic model based on the modified exponentiated Hencky energy WeHmv (solid line), Eq. (19), for different amplitudes at 1 Hz: (a) TDM 500, (b) TDM 600, and (c) TDM 800

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Fig. 11

Comparison between cyclic compression tests (markers) and the viscoelastic model based on the modified exponentiated Hencky energy WeHmv (solid line), Eq. (19), for different frequencies at 20% amplitude: (a) TDM 500, (b) TDM 600, and (c) TDM 800

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Fig. 12

Comparison between cyclic compression tests (markers) and the viscoelastic model based on the modified exponentiated Hencky energy WeHmv (solid line), Eq. (19), for different amplitudes at 1 Hz: (a) TDM 500, (b) TDM 600, and (c) TDM 800

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Fig. 13

Energy dissipation per hysteresis cycle in compression: (a) TDM 500, (b) TDM 600, and (c) TDM 800

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Fig. 14

Model parameter μA in the frequency and amplitude range: (a) TDM 500, (b) TDM 600, and (c) TDM 800

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Fig. 15

Model parameter kA in the frequency and amplitude range: (a) TDM 500, (b) TDM 600, and (c) TDM 800

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Fig. 16

Model parameter μB in the frequency and amplitude range: (a) TDM 500, (b) TDM 600, and (c) TDM 800

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Fig. 17

Comparison between compression stress corresponding to different hyperelastic models and experimental tests for different densities: (a) TDM 500, (b) TDM 600, and (c) TDM 800

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Fig. 18

Comparison between shear stress corresponding to different hyperelastic models and experimental tests for different densities: (a) TDM 500, (b) TDM 600, and (c) TDM 800

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Fig. 19

Comparison between pseudo-volumetric response for different hyperelastic models and experimental tests for different densities: (a) TDM 500, (b) TDM 600, and (c) TDM 800

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