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Hi Ruobing,

Thu, 2017-08-10 12:58

In reply to Thank you both

Hi Ruobing,

My take is that the amount of energy dissipation depends on intrinsic toughness. Higher intrinsic toughness can lead to a larger dissipation zone and hence more energy dissipation. In viscoelastic materials (e.g. Gent 1996 [15]) or materials with rate-independent hysteresis (e.g. Zhang et al. [18]), it was found that the dissipative toughness is proportional to the intrinsic toughness. Even though the magnitude of the intrinsic toughness may be tiny in comparison to the dissipative one, but an increase of the intrinsic toughness can be greatly amplified through energy dissipation and thus leads to a large increase in total toughness. In this sense, I tend to think the energy dissipation mechanism acts as an "amplifier" for the intrinsic toughness.

From a modeling perspective, a question of interest is how can we predict fracture behavior of the soft dissipative materials (e.g. for reliability analysis)? In my opinion, the local fracture criterion (e.g. a cohesive zone model at crack tip) is the best bet, since the dissipative part of the toughness can be affected by loading conditions and sample geometry. What type of traction-separation relation in the cohesive zone model should we use and does it matter? This also requires a good understanding of the local fracture process.



Thank you both

Thu, 2017-08-10 10:56

In reply to Thanks!

Dear Rong and JDI,

Thank you both for raising this interesting point! Perhaps the way of artificially deviding the fracture toughness into intrinsic and extrinsic itself is too much for many hydrogels with complex structures. In that sense, studying the local field at the crack tip directly is really appreciated to overcome this complexity.

Then the discussion brings me a question: why is the intrinsic toughness (or local crack tip field, or fatigue threshold) important for real engineering applications? We've already known how to toughen a soft material by introducing energy dissipation. Or put it in this way: why do we want to enhance the intrinsic toughness (or local material strength)? One answer to this, which I'm familiar, is the "terrible" fatigue fracture resistance of the current materials to cyclic loading (it seems that you can do no much better than the number Lake & Thomas predict). Do you have any other cases in mind?

Thanks again,


Heterogeneous material and micro-structure design

Wed, 2017-08-09 22:28

In reply to Fracture Mechanics of Soft Materials

Dear Rong,

Excellent and timely review!

Most models you summarized are at the continuum level and assume homogeneous material (my understanding may not be complete), however, these already lead to very complicated and highly nonlinear couplings among several different mechanisms, such as Mullins effect, viscoelasticity and cavitation. One question is whether the material heterogeneity plays a role in determining the crack propagation?  

Many natural biological soft materials exhibit significant material heterogeneity, anisotropy and gradient, which are believed to play important roles in reducing stress concentration and enhancing the robustness of the structures. Here is one recent paper on the material gradient in tendon-bone insertion:

Rossetti, L., L. A. Kuntz, E. Kunold, J. Schock, K. W. Müller, H. Grabmayr, J. Stolberg-Stolberg et al. "The microstructure and micromechanics of the tendon-bone insertion." Nature Materials 16, no. 6 (2017): 664-670.

A quantative understanding of how the micro- and meso-structures detrmine the overall mechanical properties, especially bulk and interface faluire is still missing.

In parallel to the great opportunities in developing accurate models and experiments to quantify the contributions to the toughness from various sources, it will also  be very important and challenging to link the micro- and meso-scale structures of the soft materials with their macro-scale mechanical properties, such as modulus, viscosity, energy dissipation and toughness. Indeed, the success of the double network hydrogel and elastomer originate from the synergistic coupling between polymer networks. Similar to your discussion with Ruobing, a further question may be how can we deliberately design the micro-structures to optimize the mechanical and physical properties of the soft tough materials? 





Wed, 2017-08-09 21:29

In reply to Dear JDI,

Dear Ruobing,

Thanks for sharing your knowledge on this point. I think Rong's comments have expressed my concern quite well. For rupture of polymer networks, it also dissipates energy to pull the chains out of the network. That's why I guess the "intrinsic" fracture energy might be rate-dependent. I am looking forward to reading your new work on this topic.

Best Regards,

Jun Luo 

Thanks! This is indeed a very

Wed, 2017-08-09 18:11

In reply to Yes. During the polydomain-to

Thanks! This is indeed a very interesting system. One more question: in the last three images you posted, the the crack has propagated but some of the material behind the crack tip should be unloaded but is still transparent. Is this some kind kinetic effect? In other words, the phase transition takes time, and has not fully occurred in the unloaded material because of the fast crack propagation?

Very nice explanations!

Wed, 2017-08-09 18:07

In reply to Dear JDI,

Hi Ruobing,

Thanks for the great points, especially on the methods to measure local toughness! I look forward to reading your paper when it comes out. To clarify, for the method based on the G-v curve, do you mean to determine G_0 by extrapolating the G-v curve to the point of v=0? 

I totally agree that there are more questions regarding the intrinsic toughness, especially on how to link the intrinsic toughness to the molecular-level failure mechanisms at crack tip. The Lake-Thomas theory is for a well crosslinked network, but for more complex networks (e.g. physically associated networks) more understandings are needed. For example, in Ref. [9] of the Jounral Club thread, Lefranc and Bouchaud studied the fracture of Agar gel (physically associated via hydrogen bonds, similar to the gelatin gel studied in Baumberger et al. 2006). Interestingly, even though the gel exibhits essentially elastic response under rheological tests (i.e. storage modulus is much larger than the loss modulus and both are rate-independent), the measured fracture toughness is still rate-dependent. This was attributed to the reptation processes of chains when being pulled out of a junction zone (analgous to a crosslinking point), i.e. the chain pull-out is resisted by neighboring chains, which may lead to an effective local viscosity. This physical picture, although still speculative, suggests that the instrinsic toughness may be rate dependent in the Agar gel. 

Dear JDI,

Wed, 2017-08-09 11:28

In reply to Thanks!

Dear JDI,

Thanks for sharing all the good thoughts and questions. Here are some of my understanding.

If we follow the literature and devide the fracture energy into intrinsic part and dissipative part, then the physical picture of the intrinsic fracture energy would be something described by Lake and Thomas in their early work (1967 Lake & Thomas). That is, theoretically the intrinsic fracture energy only depends on the chemical network (such as chain length, crosslink density, water content etc.), but not the loading rate. Such a theoretical picture is hard to verify in practice, and this is related to finding a proper method to measure the local toughness. Rong has indeed mentioned a few methods so far, and I'd like to address some further details of these methods:

(a) in [18], Zhang et. al preload the hydrogel samples to very large stretch, and then treat the samples as new materials to measure the fracture energy. The measured fracture energy is ~300 J/m2, one order of magnitude higher than the usual number that Lake-Thomas model predicts (~10 J/m2). This method is simple to implement, but it is hard to exclude the effect of viscoelastic or other dissipation from the bulk residual, even after several pre-loading cycles.

(b) in [19], Mzabi et. al use digital image correlation to capture the full strain field in the sample during fatigue fracture test, and define a length scale H0 as the size of the highly stretched zone in the undeformed state. They then use the integral of the unloading curve and pure shear test to obtain a local energy release rate. The method is innovative, but is also limited to the requirement of obtaining the visible strain field.

(c) in [20], we use the traditional fatigue fracture test to obtain the intrinsic fracture toughness (or fatigue fracture threshold), below which fatigue fracture never happens. This method is straightforward, and gives consistent number as the Lake-Thomas model (~50 J/m2), but it really requires time-consuming cyclic loading tests under many different values of stretch per cycle.

All these methods have their advantages and shortages. Related to the study of elastomers, there is also one more method to obtain the intrinsic fracture toughness. That is to measure the fracture toughness vs. crack propagation speed (so-called G-v curve). Shaoting and Rong have discussed quite a few of this under the thread already. If one has a solid theoretical model of such behavior, the intrinsic fracture toughness can be readily derived from the experimentally measured curves. A good and successful example is the study on elastomers by Gent et. al (e.g. 1994 Gent & Lai, 1996 Gent). Following this method, there is an excellent work done by Baumberger et. al (2006 Baumberger, Caroli and Martina). They actually studied the G-v curve of a physical hydrogel, and the theoretical model is quite consistent with their experimental results. Indeed, in their paper, the local fracture energy is not rate dependent, but related to the polymer-chain-pulling-out from the network after overcoming the weak interaction between them (hydrogen bonding). I guess this study partially answers your question in the last sentence. For chemically crosslinked hydrogels, however, the study on rate dependency and intrinsic fracture energy is still not quite clear.

We will have a further work to study the intrinsic fracture toughness of a same hydrogel with different values of water content, and compare the experimental results to the theoretical prediction by the Lake-Thomas model. The comparison is not perfect, but does capture the trend. The study also indicates that there is more room for the theoretical improvement beyond the Lake-Thomas model, on predicting the intrinsic fracture toughness. We will post the paper on iMechanica once it is published.

Best regards,

Ruobing Bai


Wed, 2017-08-09 05:09

In reply to Dear JDI,

Dear Rong,

Thanks for your detailed explainations! They are very informative. The physics behind the fracture of soft materials is really very rich and worthy further investigations. It might be a good method to devide the fracture energy into the "intrinsic" part (local part) and dissipative part. The correponding experiment methods to measure the local fracture energy may be very important for this area. I wonder if there are suitable methods so far.  BTW, the cohesive zone medel may be very suitable to characterize the local  fracture energy as also mentioned in the work by Prof. X. H. Zhao. It becomes difficult again if we consider the rate effect. I guess the local fracture energy in most soft materials is also rate dependent such as physical hydrogels.    


Wed, 2017-08-09 05:09

In reply to Dear JDI,

Dear Rong,

Thanks for your detailed explainations! They are very informative. The physics behind the fracture of soft materials is really very rich and worthy further investigations. It might be a good method to devide the fracture energy into the "intrinsic" part (local part) and dissipative part. The correponding experiment methods to measure the local fracture energy may be very important for this area. I wonder if there are suitable methods so far.  BTW, the cohesive zone medel may be very suitable to characterize the local  fracture energy as also mentioned in the work by Prof. X. H. Zhao. It becomes difficult again if we consider the rate effect. I guess the local fracture energy in most soft materials is also rate dependent such as physical hydrogels.    

Yes. During the polydomain-to

Wed, 2017-08-09 02:38

In reply to Dear Shengqiang,

Yes. During the polydomain-to-mondomain transition, LCE changes from isotropic state to anisotropic state with alligned mesogenic monomer. I think one neatness of such transition during fracture is its high visibility. I would like to mention that such transition is reversible with hysteresis. As you can see, after the crack extends through the entire width of the sample, the material near the crack path turns back to turbid becuase of the unloading. The dissipated energy associated with such hysteric loading and unloading contributes significantly to the fracture toughness of polydomain LCE. 

It is indeed a good idea to correlate the transparency to stress/strain state. Careful and detailed calibration may not be easy though. 

Dear Shengqiang,

Wed, 2017-08-09 01:43

In reply to Very timely review

Dear Shengqiang,

Thanks for brining up your work on the fracture of LCE. It is very interesting! In the polydomain-to-monodomain transition, does the LCE change from isotropic to anisotropic? If so, I am interested in how the transition affects the crack tip field. Also, if one can quantify the change in transparency and correlate it with some measure of stress or strain, perhaps this offers a way to probe the crack tip field as the crack opens up?

Hi Shaoting,

Wed, 2017-08-09 01:38

In reply to Hi Rong Long,

Hi Shaoting,

Thanks for the two very interesting points and the refenreces. 

1. I think delayed fracture should be associated with some kinetic processes within the material. For the two references you cited, it is due to the kinetic process of bond breaking and reformation. As you pointed out, the same process leads to viscoelasticity in the bulk material. For some hydrogels, it can also be due to the kinetic process of solvent transport, as shown in a previous work from Prof. Wei Hong's group

As for the difference between samples with and without cuts, I would think in samples witout cuts, failure can be sensitive to pre-existing defects unless they are smaller than a characteristic length scale (see a recent work from Prof. Zhigang Suo's group). Since these pre-existing defects are random in nature, one may observe a large sample-to-sample variation in the failure of samples without cuts. In contrast, in samples with cuts, the inentionally introduced crack is the dominate defect and one can obtain a much more consistent measurement of fracture toughness in this way. Prof. Wei Hong's paper has a nice discussion on this aspect. Perhaps one can better study the underlying mechanism of delayed fracture using samples with cuts. 

2. I guess for the time-temperature superposition (in terms fracture toughness versus crack propagation velocity) to work, at least three conditions are needed: i) the dissipative toughness dominates over the intrinsic one; ii) at the time-scale of interest, viscoelasticity is the main time dependent mechanism (e.g. no significant effect of poroelasticity); iii) the bulk viscoelasticity follows the time-tempreature superposition within a wide range of strain (from small to large strain) and rates. The third condition is included because conventional characterization of viscoelasticity is done at the small strain regime, but fracture can invovle large strain at the crack tip. Under large strain, the viscoelastic relaxation kinetics may be coupled to strain. In this case, the third condition may not be satisfied and I am not sure if the time-temperature superposition relation will still hold for the fracture toughness. 

Dear JDI,

Wed, 2017-08-09 00:55

In reply to toughness of soft materials

Dear JDI,

Thanks for bringing up these two issues. Here are my thoughts:

(1) For soft materials under large deformation, the crack tip field may no longer be described by the linear elastic solutions. Instead it may depend on the nonlinear consititutive relation of the soft material. Therefore, the stress intensity factor (SIF) in linear elastic fracture mechanics is no longer applicable. For hyperelastic materials, one can obtain asymptotic solutions of the crack tip field and identify the amplitude of such asympotic solutions as the "SIF". But such definitions depend on the detailed form of the hyperelastic model, and thus may not be very useful. 

On the other hand, J-integral is still well defined for hyperelastic materials. Because of large deformation, J-integral should be written with respect to the reference configruation. It is equal to the energy release rate if the crack propagates straightly ahead.

If hysteresis is present, J-integral becomes tricky to interpret. The common practice is to use the critical energy release rate as a fracture criterion. Things can get more complicated for dissipative materials because the critical energy release rate to initiate crack growth and to to maintain a steady-state crack growth may be different. In this case, one may measure the energy release rate as a function of crack extension length, i.e. the crack growth resistance curve. 

(2) This is a great point. In a pure shear fracture test, the energy release rate can be calculated as G = W*H where H is the height of the sample. For hyperelastic materials, W is the strain energy density for material points far ahead of the crack tip. For dissipative materials with hysteresis, W should be interpreted as the work per unit volume doen to material points far ahead of the crack tip (e.g. see Section 3 of our recent paper). The critical value of G upon steady-state crack growth is the fracture toughness. 

With this definition, the fracture toughness is in general not a material parameters. It includes two terms: an intrinsic toughness associated with material failure processes at the crack tip and a dissipative toughness for the energy release rate consumed in a dissipation zone surronding the crack tip. The instrinsic toughness may be a material parameter (i.e. a local fracture criterion) but the dissipative one is not. For viscoelastic materials, the latter depends on crack velocity and temperature. If the dissipation zone size is comparable to the sample size, the dissipative toughness may depend on sample size too. For material with rate-independent damage (e.g. Mullin's effect), the dissipative toughness also depends on prestretch (e.g. see Zhang et al.). However, it is very challenging to separately measure the intrinsic and dissipative toughness in experiments. Most experimental measurements so far can only provide a total fracture toughness. On the other hand, there have been many theoretical and computational efforts to solve this problem as discussed in the Journal Club. 

"Suddenly the "hardening" of

Mon, 2017-08-07 19:52

In reply to Griffith was an incredible man

"Suddenly the "hardening" of materials due to processes such as cold rolling were no longer mysterious."

Griffith did not explain strain hardening as suggested here.

Abaqus mailing list

Mon, 2017-08-07 13:44

In reply to help to wright umat for multi yield surfaces j2 plasticity model

Subscribe to and seek assistance from the
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nearest node

Mon, 2017-08-07 13:43

In reply to Abaqus/Python - commands to find nearest node to a given point

The question was also adressed on

I attach a script with instruction from an old Abaqus site.




Find Nearest Node Plug-in




NOTE: This plug-in has undergone testing and is expected to work with the version of Abaqus that it is shipped with.  However, the level of testing is not as stringent as that for the Abaqus products in general.  Limited support will be available from Dassault Systemes, for this plug-in, and it may not be available with future Abaqus releases.








This plug-in locates the node in a model database (MDB) or output database (ODB) that is nearest to a specified coordinate point.  The plug-in works with meshed models (in an MDB) and undeformed plots (in an ODB); the plug-in does not work with deformed plots in an ODB. 




For large models, you can specify the area of the model to search by selecting a subset of nodes from the viewport.








To install the plug-in, unzip and save the contents of the attached archive to one of the following directories:


  • abaqus_dir\cae\abaqus_plugins, where abaqus_dir is the ABAQUS parent directory
  • home_dir\abaqus_plugins, where home_dir is your home directory
  • current_dir\abaqus_plugins, where current_dir is the current directory




After installing the plug-in, start Abaqus/CAE and enter any assembly-related module or the Visualization module.  Find Nearest Node is available in the Plug-ins menu on the main menu bar (Plug-insàAbaqusàFind Nearest Node).








Enter the X, Y, and Z coordinates for the starting point.  Click Find to highlight in the viewport the node nearest to the specified starting coordinates.  Click the Select Nodes for Reduced Search button and select nodes in the viewport to limit your search to a particular area of the model.







When searching in reduced mode, only nodes on one instance can be selected.


from abaqusGui import *
import _abqPluginUtils, os
thisPath = os.path.abspath(__file__)
thisDir = os.path.dirname(thisPath)

# Use package syntax to avoid possible name clashes with other plugins
from abq_FindNearestNode.nearestNodeForm import NearestNodeForm

# Register commands
version = '2.1-1'
status = _abqPluginUtils.checkCompatibility('Find Nearest Node', version)
if status == 'OK':
        buttonText='Abaqus|Find Nearest Node...',
        kernelInitString='import abq_FindNearestNode.nearestNodeModule',
        applicableModules=["Assembly","Step","Interaction","Load","Mesh","Job", "Visualization"],
        author='Dassault Systemes',
        description='This plug-in finds the nearest node to a given point.',
        helpUrl=os.path.join(thisDir, 'abq_FindNearestNode', 'NearestNode_help.html'),

Is the link VT08 still

Mon, 2017-08-07 10:49

In reply to Griffith's originality and controversy

Is the link VT08 still working? It is not opening on my computer.

Hi every one. Im working on

Sun, 2017-08-06 03:40

In reply to Need user material Fortran code for viscoelastic

Hi every one. Im working on multi yield surfaces j2 plasitisity and if its possible i want add cappability to predict time dependant hehaivior of geomaterials. to start i must wright an umat code for multi yield surfaces j2 model. please help me how can i find it or give me any information about it. thanks for every one.


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