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Research Papers

# Nonhyperelastic Nature of an Elastomeric High Strain Material

[+] Author and Article Information
Choon-Sik Jhun1

Department of Biomedical Engineering, Texas A&M University, College Station, TX 77843-3120csjhun@gmail.com

John C. Criscione

Department of Biomedical Engineering, Texas A&M University, College Station, TX 77843-3120

1

Corresponding author.

J. Appl. Mech 77(6), 061014 (Sep 01, 2010) (6 pages) doi:10.1115/1.4001250 History: Received September 25, 2008; Revised December 07, 2009; Published September 01, 2010; Online September 01, 2010

## Abstract

Rubber materials have mostly been modeled by utilizing hyperelasticity, which have led to greater understanding and acceptable predictability of their stress-strain response. However, inherent inelastic behavior excluded by approximation has never been characterized by time-dependent parameters such as time, strain-rate, and strain history. We hypothesized that time, stretch rate, and stretch history were prominent factors that induce the inelasticity, and we characterized the inelasticity in terms of those factors using a randomized stretch-controlled testing protocol. We applied the custom randomized testing protocol with the fundamental statistical theory to characterize inelastic behavior imbedded in the high strain material. We hypothesized that time spent testing $(T)$, rate-related stretch history $(Ht2)$, and long-term stretch history $(Ht1)$ give rise to the inelastic deviation from hyperelasticity. We examined the significance, effectiveness, and differences of $T$, $Ht2$, and $Ht1$ by looking at the derived multivariable linear regression models. Distribution of prediction deviation was also examined to see if we missed any other significant variable. Predictability of the multivariable linear regression models was validated by utilizing the unused data from the randomized testing protocol and data from the conventional cyclic testing protocol. We found that the inelasticity of the rubber-like material is highly related to $T$, $Ht2$, and $Ht1$, but not equally influential to all stretches. At smaller deformations, greater inelastic deviation occurs. Inelasticity exponentially decreased over stretch and was nonlinearly related to time. This study successfully determined the elastic/inelastic responses and factors that induce the inelastic response of the rubber-like material. This investigation suggests a way to better describe the elastic/inelastic properties and phenomenological models of rubber-like materials.

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Copyright © 2010 by American Society of Mechanical Engineers
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## Figures

Figure 1

A randomized stretch and stretch rate testing protocol. Upon inputting the reference length of the sample, the stretch versus time protocol was converted to displacement versus time and fed to opposing actuators.

Figure 2

The randomized stretch-controlled protocol and corresponding force output profile for the rubber fiber

Figure 3

Stresses and average stress at each nominal stretch. The black dots represent the hyperelastic stress responses. Discrepancy between stresses and average stress at each nominal stretch demonstrates inelastic behavior of the rubber fiber.

Figure 4

Fractional deviation FU that represents the inelasticity for λ=1.1, 1.3, 1.5, 1.7, and 1.9 were 11.59%, 3.59%, 2.80%, 1.26%, and 1.19%, respectively. The degree of inelasticity was greater at low stretches and exponentially decreased.

Figure 5

Loading and unloading curves of the cyclic testing protocol. Hysteresis is evident in cyclic loading testing.

Figure 6

Fractional deviation from cyclic loading testing. Fractional deviation FU for λ=1.1, 1.3, 1.5, 1.7, and 1.9 were 5.82%, 1.51%, 1.01%, 1.1%, and 0.89%, respectively. Degree of inelasticity was greater at low stretches and exponentially decreased for both the randomized and cyclic testing protocols.

Figure 7

(a) Inelastic deviation and (b) prediction deviation associated with T for λ=1.1. (c) Inelastic deviation and (d) prediction deviation associated with Ht2 for λ=1.1.

Figure 8

Prediction of inelastic deviations from cyclic tensile testing for (a) λ=1.1, (b) λ=1.3, (c) λ=1.5, (d) λ=1.7, and (e) λ=1.9 (vertical lines represent a confidence interval)

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