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Research Papers

Pseudoelasticity and Nonideal Mullins Effect of Nanocomposite Hydrogels

[+] Author and Article Information
Jingda Tang, Xing Chen

State Key Laboratory for Turbulence
and Complex Systems,
College of Engineering,
Peking University,
Beijing 100871, China

Yongmao Pei

State Key Laboratory for Turbulence
and Complex Systems,
College of Engineering,
Peking University,
Beijing 100871, China
e-mail: peiym@pku.edu.cn

Daining Fang

State Key Laboratory for Turbulence
and Complex Systems,
College of Engineering,
Peking University,
Beijing 100871, China;
Institute of Advanced Structure Technology,
Beijing Institute of Technology,
Beijing 100081, China;
State Key Laboratory of Explosion Science
and Technology,
Beijing Institute of Technology,
Beijing 100081,China
e-mail: fangdn@pku.edu.cn

1Corresponding authors.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received June 22, 2016; final manuscript received August 20, 2016; published online September 9, 2016. Editor: Yonggang Huang.

J. Appl. Mech 83(11), 111010 (Sep 09, 2016) (10 pages) Paper No: JAM-16-1315; doi: 10.1115/1.4034538 History: Received June 22, 2016; Revised August 20, 2016

The polymer network of a nanocomposite (NC) hydrogel is physically crosslinked by nanoclay. Recently reported high toughness of nanocomposite (NC) hydrogels highlights the importance of their dissipative properties. The desorption of polymer chains from clay surface may contribute mostly to the hysteresis of NC hydrogels. Here, we proposed a mechanistically motivated pseudoelastic model capable of characterizing the hysteresis of NC hydrogels. The two parameters in the proposed damage variable can be determined by the experiments. We applied the model to the uniaxial tension and reproduced the ideal Mullins effect of NC hydrogels. Furthermore, we considered two nonideal effects: residual deformation and nonideal reloading in multicycle test, using newly proposed damage parameters. A power law with the order of 1/3 is established between the residual fraction of the stretch and the re-adsorption ratio of polymer chains. Finally, we demonstrated the dissipative properties of various NC hydrogels with the model.

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Figures

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Fig. 3

The bonds between polymer chains and clay sheets determine the dissipation of NC hydrogels. (a) The hysteresis increases as the bonds weaken. (b) The hysteresis increases as the distribution width m decreases, where W0 = 25 kJ/m3. (c, d) The dissipation energy U is proportional to the square of the maximum stretch λm for different W0 and m, respectively. (e,f) The characteristic dissipation function increases as the bond energy densities (e) and distribution widths (f) decrease. Experimental data are calculated from our previous work [20].

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Fig. 2

The hysteresis and ideal Mullins effect of NC hydrogels. (a) Hysteresis at different deformations of λm = 4, 8, 12, 16; scatters are experimental data [20]. (b) The comparison of the softening variable η between theory and experiment (scatters) [20]. (c) The loading history for the Mullins effect. (d) The ideal Mullins effect in theory and the nonideal Mullins effect in experiment for NC hydrogels [20].

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Fig. 1

The schematic of the Mullins effect (a) and the dissipative mechanism of NC hydrogels (b). At reference state, clay sheets are randomly dispersed; while at deformed state, polymer chains will slip on the surface of clay sheets and make the desorption happen to induce hysteresis.

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Fig. 4

The physical mechanism on the residual deformation of NC hydrogels. The competition between retained chains and re-adsorbed chains causes the residual deformation.

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Fig. 5

Residual deformation of NC hydrogels. (a) Hysteresis at different deformations of λm = 4, 8, 12, 16; scatters are experimental data [20]. (b) The comparison of the softening variable between theory and experimental data.

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Fig. 6

Re-adsorption of polymer chains affects the residual deformation of NC hydrogels. (a) Hysteresis of NC hydrogels with different re-adsorption ratios of R = 0, 0.05, 0.25, 1. (b) The residual stretch λr increases linearly with the maximum stretch λm for different R. (c) A power law with the order of 1/3 is established between the residual fraction λr/λm and the re-adsorption ratio R.

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Fig. 7

The hysteresis of NC hydrogels in multicycle test with different reloading stretches Δλ. (a) Δλ = 1.5 (b) Δλ = 2 (c) Δλ = 2.5, and (d) Δλ = 3. Experimental data are from our previous work [20].

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Fig. 8

A nonideal Mullins effect of NC hydrogels with both residual deformation and the hysteresis between the reloading and unloading stage. Experimental data are from our previous work [20].

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Fig. 11

The preconstant C shows very weak dependence on the maximum stretch λm and the re-adsorption ratio R

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Fig. 9

The prediction on the dissipation of various nanoparticle-filled materials. (a) PNIPAm /Laponite XLS and PAAm/Laponite XLS nanocomposite hydrogel [46], (b) PDMA/Laponite XLS nanocomposite hydrogel [14], (c) PDMA/Silica hydrogel [17], and (d) carbon-black filled rubber [43].

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Fig. 10

The parameters in the softening variable η determine the dissipative properties of NC hydrogels (a,c). The probability of fracture and the damage fraction of NC hydrogels when the most probable bond energy density W0 is changed (b,d). The probability of fracture, and the damage fraction of NC hydrogels when the distribution width m is changed.

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