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Research Papers

A Constitutive Model for Soft Materials Incorporating Viscoelasticity and Mullins Effect

[+] Author and Article Information
Tongqing Lu

State Key Lab for Strength and
Vibration of Mechanical Structures,
Shaanxi Engineering Laboratory for Vibration
Control of Aerospace Structures,
Department of Engineering Mechanics,
Xi'an Jiaotong University,
Xi'an 710049, China

Jikun Wang, Ruisen Yang

State Key Lab for Strength and
Vibration of Mechanical Structures,
Department of Engineering Mechanics,
Xi'an Jiaotong University,
Xi'an 710049, China

T. J. Wang

State Key Lab for Strength and
Vibration of Mechanical Structures,
Department of Engineering Mechanics,
Xi'an Jiaotong University,
Xi'an 710049, China
e-mail: wangtj@mail.xjtu.edu.cn

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received October 8, 2016; final manuscript received November 4, 2016; published online November 22, 2016. Editor: Yonggang Huang.

J. Appl. Mech 84(2), 021010 (Nov 22, 2016) (9 pages) Paper No: JAM-16-1493; doi: 10.1115/1.4035180 History: Received October 08, 2016; Revised November 04, 2016

Soft materials including elastomers and gels are widely used in applications of energy absorption, soft robotics, bioengineering, and medical instruments. For many soft materials subject to loading and unloading cycles, the stress required on reloading is often less than that on the initial loading, known as Mullins effect. Meanwhile, soft materials usually exhibit rate-dependent viscous behavior. Both effects were recently reported on a new kind of synthesized tough gel, with capability of large deformation, high strength, and extremely high toughness. In this work, we develop a coupled viscoelastic and Mullins-effect model to characterize the deformation behavior of the tough gel. We modify one of the elastic components in Zener model to be a damageable spring to incorporate the Mullins effect and model the viscous effect to behave as a Newtonian fluid. We synthesized the tough gel described in the literature (Sun et al., Nature 2012) and conducted uniaxial tensile tests and stress relaxation tests. We also investigated the two effects on three other soft materials, polyacrylate elastomer, Nitrile-Butadiene Rubber, and polyurethane. We find that our presented model is so robust that it can characterize all the four materials, with modulus ranging from a few tens of kilopascal to megapascal. The theory and experiment for all tested materials agree very well.

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Figures

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Fig. 1

(a) Nominal stress–stretch curves of the tough gel under uniaxial cyclic loading at different loading rates and (b) nominal stress–stretch curves of the tough gel under multiple uniaxial cyclic loading

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Fig. 2

Rheological model with Mullins effect: (a) a damageable spring in series with a Kevin unit and (b) a damageable spring in parallel with a Maxwell unit

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Fig. 3

(a) Samples of four different materials and (b) Shimadzu tensile tester

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Fig. 4

Nominal stress–stretch curves for uniaxial tension tests at a nominal strain rate 3.33×10-3/s : (a) tough gel, (b) VHB, (c) NBR, and (d) PU. The dots are experimental data and the solid lines are theoretical predictions.

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Fig. 5

Representative profile of the history of applied stretch in stress relaxation tests

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Fig. 6

Experimental results and theoretical predictions for stress relaxation tests of the tough gel under different loading rates (a), (c) stress–stretch curves and (b), (d) stress-time history

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Fig. 7

Experimental results and theoretical predictions for stress relaxation tests of VHB under different loading rates

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Fig. 8

Experimental results and theoretical predictions for stress relaxation tests of NBR under different loading rates

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Fig. 9

Experimental results and theoretical predictions for stress relaxation tests of PU under different loading rates

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Fig. 10

Comparisons of stress–stretch curves for the tough gel under different loading rates. The curve under the loading rate 3.33×10-3/s is from the uniaxial tensile test. The curves under the other two loading rates are from the stress relaxation tests.

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