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Research Papers

A Phenomenological Model for Shakedown of Tough Hydrogels Under Cyclic Loads

[+] Author and Article Information
Zhongtong Wang, Jingda Tang, Wenlei Zhang, Tongda Lian, Tiejun Wang

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

Ruobing Bai

John A. Paulson School of Engineering
and Applied Sciences,
Kavli Institute for Bionano
Science and Technology,
Harvard University,
Cambridge, MA 02138

Tongqing Lu

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

1Z. Wang and J. Tang contributed equally to this work.

2Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received April 6, 2018; final manuscript received May 11, 2018; published online June 14, 2018. Assoc. Editor: Junlan Wang.

J. Appl. Mech 85(9), 091005 (Jun 14, 2018) (8 pages) Paper No: JAM-18-1193; doi: 10.1115/1.4040330 History: Received April 06, 2018; Revised May 11, 2018

Most tough hydrogels suffer accumulated damages under cyclic loads. The damages may stem from breakage of covalent bonds, unzipping of ionic crosslinks, or desorption of polymer chains from nanoparticle surfaces. Recent experiments report that when a tough hydrogel is subject to cyclic loads, the stress–stretch curves of tough hydrogels change cycle by cycle and approach a steady-state after thousands of cycles, denoted as the shakedown phenomenon. In this paper, we develop a phenomenological model to describe the shakedown of tough hydrogels under prolonged cyclic loads for the first time. We specify a new evolution law of damage variable in multiple cycles, motivated by the experimental observations. We synthesize nanocomposite hydrogels and conduct the cyclic tests. Our model fits the experimental data remarkably well, including the features of Mullins effect, residual stretch and shakedown. Our model is capable of predicting the stress–stretch behavior of subsequent thousands of cycles by using the fitting parameters from the first and second cycle. We further apply the model to polyacrylamide (PAAM)/poly(2-acrylanmido-2-methyl-1-propanesulfonic acid) (PAMPS) and PAAM/alginate double-network hydrogels. Good agreement between theoretical prediction and experimental data is also achieved. The model is hoped to serve as a tool to probe the complex nature of tough hydrogels, through cyclic loads.

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Figures

Grahic Jump Location
Fig. 1

Typical stress–stretch curves of tough hydrogels under cyclic loadings

Grahic Jump Location
Fig. 2

Stress–stretch curves of the nanocomposite hydrogel under cyclic loads with different maximum stretches (a) λmax = 3.0, (b) λmax = 3.5, (c) λmax = 4.0, and (d) λmax = 4.5. (e) The maximum stress decays over cycles. (f) The stress–stretch curves of the 2000th cycle.

Grahic Jump Location
Fig. 3

The comparisons between the experimental results and theoretical predictions for nanocomposite hydrogels in (a) the first cycle, (c) the second cycle, (e) the third cycle and (g) the Nth cycle. (i) Comparison on the gradual decrease of stress. ((b), (d), (f), (h), and (j)) Comparisons with another set of experimental results with λmax = 4.5.

Grahic Jump Location
Fig. 4

The comparisons between the experimental data and theoretical predictions for ((a), (c), and (e)) PAAM/PAMPS hydrogels and ((b), (d), and (f)) PAAM/alginate hydrogels

Grahic Jump Location
Fig. 5

(a) Stress–stretch curves predicted by the model with the fitting parameters of nanocomposite hydrogels (b) the parameter that represents stress decay changes to γ = 0.02, (c) the parameters that determine the residual stretch change to ν1 = 0.04, ν3 = 4.0

Grahic Jump Location
Fig. 6

Stress–stretch curves of the 2000th cycle under different maximum stretches with the fitting parameters of nanocomposite hydrogels

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