Thanks, Shaoting. This is convincing.

Interesting point. Thanks, Ruobing!

Hi Ruobing,

You made great points and pointed out more evidence. Thanks!

Also, I totally agree with you that hydrogel can be a very good platform to expereimentally and theoretically explore new material design and advance our understanding of relation between the microscale structures and macroscopic mechanical behaviors.

Best,

Teng

Hi Ruobing,

I highly enjoy reading a set of papers from your group, especially for fatigue fracture. It turns out that the intrinsic fracture energy is the parameter as important as total toughness, which is relavent to long-term performance for practical applications.

Best,

Shaoting

Dear Lihua,

The fracture toughness of a hydrogel can greatly depend on a lot of things. Start from simple things, for example, the crosslink density, as Shaoting mentioned. For PAAm hydrogels, if the crosslink density is low enough, the toughness is measured to be over 400 J/m2 with pure shear tests. Interesting, right? We frequently mentioned in papers that PAAm gels are brittle or weak, but in fact its toughness is not bad at all! Even for Gong's original DN gel, it was initially only hundreds of J/m2. However, in the fatigue paper by Zhang et. al, the fracture toughness can also be enhanced to thousands of J/m2.

As a result, 400 J/m2 for intrinsic toughness seems very high, but not quite suprising, depending on how the gel is made. Maybe in the end they are just gels with different compositions, not necessarily any special unknown interactions (but of course it could be important as well).

I think fracture of soft materials in general is still a big topic to explore. From purely scientific view, hydrogels provide a platform, where one can easily tune the compositions and relate them to macroscopic mechanical behaviors. This was hard to imagine at the age of stiff materials like metals.

Best,

Ruobing

Hi Lihua,

I agree with you that it is not fully unerstood why the toughness of the pre-damged PAAm-alginate gel can be higher than PAAm gel. Our model captured the toughness enhancement due to the Mullins effect if we chose the toughness of pre-damaged (nearly to the failure point) as a rerfence. This is the reason we define it as the intrinsic toughness. I think there may be other mechanism contributing the toughness enhacment as well, which calls for a multiscale modeling and experimental study.

I enjoyed reading Gong's work on hydrogels. Depending on the fabrication process and material combination, double netwrok gels may have different microstructures. We may be able to link some of some designed materials to the pre-damaged PAAm-alginate gel and even directly observe detailed distributions of the hard phases in the double network hydrogels. The research of soft tough materials is under rapid development, and I hope we can achieve better understanding on these puzzles from micro- and nao-scales.

Best,

Teng

Dear Lihua,

Thanks for raising this question. In addition to Teng's explanation,I would like add a few more points.

1. When the network is highly stretchable, the intrinsic fracture energy can reach the order of 100J/m^2. I measure the fracture energy of single network of PAAm with 15 wt% polymer concetration and 0.01 wt% crosslinker. The fracture energy was measured to be 180J/m^2.

2. As teng mentioned, the PAAm-alginate system is not just a mixture of PAAm netwrok with alginate moleculars. The interaction between alginate and PAAm may give the additional reinforcement to the single PAAm network. Prof. Suo's group recently proposed to perform fatigue test to identify the threshold, which is corresponding to the intrinsic fracture energy. Zhang, Wenlei, et al. "Fatigue of double-network hydrogels." Engineering Fracture Mechanics (2017) measured the critical threshold fracture energy of fatigue for PAMPS/PAAM double network (two interpenetrating covalent network). The threshold is measured to be 400J/m^2 for the system with PAAm of low crosslinker density and 200J/m^2 for the system with PAAM of high crosslink density. The number is also larger than the intrinsic fracture energy of each single network, which might be due to the interaction between the two networks as well.

3. Lake Thomas picture give quanlitative prediction on the intrinsic fracture energy of a polymer chain network. Sakai (Akagi, Yuki, et al. "Fracture energy of polymer gels with controlled network structures." The Journal of chemical physics 139.14 (2013): 144905.) measured fracture energy of ideal network, which shows that there is a perfactor of ~3 for the quantitative calculation of intrinsic fracture energy.

Indeed, How to quantitative calculate and measure the intrinsic fracture network of hydrogel needs effort to be elucidated.

Best,

Shaoting

Teng, thanks for the explanation. Although I am not fully convinced, I can't think of other reasons. However, Gong's original double network gels have a toughness a few hundred J/m2.

Hi Lihua,

Thanks for your great question. The 400J/m2 is indeed higher than the normal PAAm hydrogel. It also puzzles us, and we think it is very likely related to the microstructures of a double network hydrogel (e.g., PAAm-alginate) after pre-damaged deformation.

You can see from our EML paper that the toughness of PAAm-alginate gel indeed exhibited a plateu as we increased the pre-stretch before introducing a main crack into the sample. The plateu was taken as the intrinsic fracture energy of PAAm-alginate, and gave the value of 400J/m2 for the gel we used in Fig. 5. Our guess is that the broken brittle components (alginate and/or bonding between alginate and PAAm) in the double network hydrogel may be still larger than the small alginate moleculars. They may form some meso-scale stiff fillments to reinforce the PAAm matrix. So, we should still think the pre-damaged PAAm-alginate gel as a composite of soft and hard phases, not just a mixture of PAAm netwrok with alginate moleculars.

This picture definitely needs more experimental and modeling efforts to validate and is worthwhile for more in-depth studies. Also, it seems the PAAm hydrogel can be tuned (e.g., chain length and crosslinkers) to have a little higher toughness, such as higher than 10 J/m2. But definitely, the toughness of PAAm hydrogel itself we used in our paper is much lower than 400 J/m2. Shaoting did the experiments, and he may have more information.

Thanks.

Best,

Teng

Teng, thanks for sharing the files. I have one question about the intrinsic fracture energy. You experimentally measured T0=400J/m2, which is much higher than that of normal hydrogels. How to understand this?

Dear Ruobing,

Thanks for your nice words.

Best,

Teng

Deat Teng,

Thank you for sharing these files. It is a big contribution to the community.

Best regards,

Ruobing

Hi Jinxiong,

Your questions are very intersting and challenging. The current input file for adhesion can only simulate the interfacial failure. The co-exist of bulk material failure (e.g., fracture and cavitation) and interfacial failure is very complicated. For this kind problem, new modeling and simulation techniques should be ued. Phase field may be one of the promising methods, but I do not have too much experience on it. The Zig-Zag pattern you referred also needs a fully 3D simulations, which can result in a very large simulation.

Even in interfacial failure, various patterns can exist and be found in a review by Animangsu and Chaudhury (Ghatak, Animangsu, and Manoj K. Chaudhury. "Adhesion-induced instability patterns in thin confined elastic film." Langmuir 19, no. 7 (2003): 2621-2631). The cohesive zone model is promising to capture such kinds of instabilities, but may also require a very large scale simulation.

These are all important and challenging questions and definitely call for more studies.

Best,

Teng

Dear jinxiong,

Thanks for your interests in our work. The modified Ogden-Roxburgh is already implemented in ABAQUS. The original Ogden-Roxburgh was based on fully icompressible materials, and the modification is to apply the softening to the deviatoric part only for compressible materials. You can find a detailed description in ABAQUS manual

http://abaqusdoc.ucalgary.ca/v6.9/books/usb/default.htm?startat=pt05ch18...

Best,

Teng

Dear Teng, another question regarding the modeling of adhesion of hydrogels to a rigid substrate. Peeling of soft materials from a bonded rigid substrate may exhibit various patterns. Fracture may occur along the interface of hydrogel and substrate, and this is the interfacial fracture. However, in some cases fracture may occur in the soft materials itself and the peeling results in Zig-Zag fracture pattern. Can your model capture this fracture patterns?

Thanks,

Jinxiong

Dear Teng, Thank you very much for sharing your ABAQUS files for coupling of Mullins effect and cohesive zone model. These files are very helpful for beginners of learing this fantastic topic and use of ABAQUS to model soft materials. You and Xuanhe made great contribution to the community.

One quick question regarding your EML paper. You mentioned you implement a modified Ogden-Roxburgh model. How did you do that? You directly use the Mullins model provided by ABAQUS or you write a user-subroutine?

Thanks,

Jinxiong