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Updated: 5 hours 49 min ago

Seems the link is not

Mon, 2021-05-03 16:13

In reply to Nice work, but I think an

Seems the link is not correctly reflected: 

Rao C, Sun H, Liu Y. Physics informed deep learning for computational elastodynamics without labeled data. arXiv preprint arXiv:2006.08472. 2020 Jun 10.


Nice work, but I think an

Mon, 2021-05-03 16:11

In reply to Exact imposition of boundary conditions in physics-informed neural networks

Nice work, but I think an important and very similar work is left out: 

Spallation of polymers

Mon, 2021-05-03 13:04

In reply to Atomic-Scale Investigation on the Mechanical Behavior of Ultrathin Multilayers Under Shock Loading

A presentation (~11 mins) from our work on the spallation of polymers (ref. [5]) is available here:


Mon, 2021-05-03 12:35

In reply to Energy absorption mechanisms of nanoscopic multilayer structures under ballistic impact loading

A presentation (~10 mins), based on this work, is available here:

Thanks for sharing.

Thu, 2021-04-29 12:34

In reply to Writing tips

Thanks for sharing.

Dear Prof. Xu,

Thu, 2021-04-29 06:00

In reply to Journal Club For April 2021: Variational phase-field modeling of brittle and cohesive fracture

Dear Prof. Xu,

I have sent you an email regarding your suggestion. 

Best regards,


Hi All there, if you have any

Thu, 2021-04-29 04:44

In reply to MoFEM: School on Advanced Topics in Computational Mechanics (UKACM 2021)

Hi All there, if you have any comments? You like to try, the easiest why try is to see examples on Google Colab,


2. Poisson's problem (Google Colab)

3. Linear Acoustics (Google Colab)


Experimental validation on crack nucleation and propagation

Wed, 2021-04-28 20:44

In reply to Journal Club For April 2021: Variational phase-field modeling of brittle and cohesive fracture

Dear Profs. Nguyen and Wu,

Interesting simulation approach. As an experimentalist on fracture and impact mechanics, I always try to learn some new simulation tools,  especially XFEM, CZ and PD cannot simulate my previous dynamic fracture experiments well.

For example, I have some unique crack nucleation (from zero length to a finite length), crack branching (branching angle is larger than the max. theoretical angle), sharply curved cracks which exceed the simulation capability of XFEM.  

I found you’re simulating old crack branching experiments in 1991. I suggest that we may have collaboration in the future. I attached three papers on dynamic fracture experiments co-authored with Prof. Rosakis at the California Institute of Technology.

1 L. R. Xu and A. J. Rosakis,  “An Experimental Study on Dynamic Failure Events in Homogeneous Layered Materials Using Dynamic Photoelasticity and High-speed Photography,” Optics and Laser in Engineering, Vol. 40, pp. 263-288,2003. ( PDF file)

2. L. R. Xu, Y. Y. Huang and A. J. Rosakis, “Dynamic Crack Deflection and Penetration at Interfaces in Homogeneous Materials: Experimental Studies and Model Predictions,” Journal of the Mechanics and Physics of Solids, Vol. 51, pp.425-460, 2003. ( PDF file)

3. L. R. Xu and A. J. Rosakis, “Real-time Experimental Investigation of Dynamic Crack Branching Using High-speed Optical Diagnostics,” SEM Experimental Techniques, Vol. 27,pp.23-26, 2003. (PDF file)

My email is Look forward to meeting you in the future.    

Roy Xu

Can Zerilli–Armstrong model or Johnson-Cook

Tue, 2021-04-27 16:22

In reply to Interesting review

Dear Prof. Yang;

Both of these models you mention are empirical curve fitting models. If you have a test data you can fit them to these functions and even if they don't work you can add new parameters to curve fit to your data. In my humble opinion, that is not science. I realize that, now it is called "Data Science".  :-)

Best Regards

Cemal Basaran

3D Hashin failure criteria with exponential damage evolution

Tue, 2021-04-20 03:41

In reply to Sharing ABAQUS UMAT and VUMAT subroutines

If you are looking to use the Hashin 3D criterion with exponential damage evolution, the following VUMAT subroutine is applicable in Abaqus software. You can get it for a small fee.

There is a Ph.D. opening in

Mon, 2021-04-19 13:43

In reply to Ph.D. position at the Mechanical Engineering Department of University of Houston

There is a Ph.D. opening in my research group in the Mechanical Engineering department at the University of Houston to be filled as soon as possible.
The research topic is multiscale modeling of the deformation response of SMAs through Machine Learning and Bayesian Inference.

Interested applicants are requested to contact Theocharis Baxevanis ( with a brief cover letter that includes a summary of skills and copy of CV.
A master's degree in the areas of computational/continuum/fracture mechanics is required.

Yes. Thank you again for your

Mon, 2021-04-12 05:53

In reply to I think that, the H history

Yes. Thank you again for your sharing! :)



I think that, the H history

Mon, 2021-04-12 04:43

In reply to Journal Club For April 2021: Variational phase-field modeling of brittle and cohesive fracture

I think that, the H history variable is an easy way to impose that below certain level of deformation there is no fracture/damage. Is it ok for you?

Interesting review

Sun, 2021-04-11 22:35

In reply to A Review of Damage, Void Evolution, and Fatigue Life Prediction Models

Dear Prof. Cemal Basaran,

Thanks for sharing. Can I ask you a question?

Can Zerilli–Armstrong model or Johnson-Cook model predict localized plastic failure or damage such as shear band failure or necking failure and location? Like our recent work   " Revisit initiation of localized plastic deformation: Shear band & necking "     

I am new and but also very interested in fatigue life prediction models for metals and polymers. Is there any work relate to fatigue damage to microstuctural changes of metals or polymers?

Thank you again,


Thank you for your reply

Sun, 2021-04-11 11:48

In reply to Dear Tianyu,

Dear Prof. Nguyen and Prof. Wu


Thanks for your reply! I think you have made it clear. I can see now why your algorithm set a lower bound for the history variable H. So you are trying to use that lower bound for H to set d=0 outside the crack band so that you can create the band automatically. It looks very cool! But I still have one question, is this technique used just for a numerical purpose? Does it have any physical meaning?  


Best Regards,


Dear Tianyu,

Sun, 2021-04-11 01:14

In reply to Journal Club For April 2021: Variational phase-field modeling of brittle and cohesive fracture

Dear Tianyu,

Equations (1,2) hold for the entire domain, just that outside the damged region B, d=0 identically. The reason that Jian-Ying always write (1,2) because he wanted to emphasize that the damage equation is confined only to B, a much smaller sub-domain. Plus, in our implementation, we exploit this fact to have two sub-domains: B where elements with damage dofs and the remaining with elements without damage dofs.

We can have d=1, I do not see any problem with that.



Questions about governing eq

Sat, 2021-04-10 09:24

In reply to Journal Club For April 2021: Variational phase-field modeling of brittle and cohesive fracture

Dear Prof. Nguyen and Prof. Wu


Thank you for your sharing. I am reading your work recently and have several questions about the governing equations. According to your paper [1], the governing equations for phase-field are as follows,

However, these governing equations only apply in the localization band domain. The governing eq for the domain outside the band is not given. Besides, in the initial elastic stage, there is no localization band. So what is the governing equation then? If I understand the problem correctly, the governing equations for the domain outside the band and for the elastic stage are [2]

Due to α'(0)>0, we have d=0 outside the localization crack band all the time. This is also the reason why α(d)=2d-d^2 leads to an elastic stage while α(d)=d^2 doesn't.  If I made mistakes, please point them out. 

Here comes the first question, you said in your paper [3] that "However, this strategy is not necessarily mandatory. When the damage sub-domain Bh cannot be easily selected, the whole computational domain Ωh can be used." Do you mean that the governing eq (1-2) can be applied to the whole computational domain? If so, can you explain the reason? From my point of view, eq(1-2) is not equivalent to eq(3-4) outside the crack band. 

The second question is for eq (1-2), there is a trivial solution d=1 in B. So how to avoid this solution in computation? 

I am new to this area and if you could answer my questions I will appreciate it very much.


Best Regards,




[1] Jian-Ying Wu, Yuli Huang, Hao Zhou, Vinh Phu Nguyen, Three-dimensional phase-field modeling of mode I + II/III failure in solids, Computer Methods in Applied Mechanics and Engineering, Volume 373, 2021, 113537, ISSN 0045-7825,

[2] Jian-Ying Wu, A unified phase-field theory for the mechanics of damage and quasi-brittle failure, Journal of the Mechanics and Physics of Solids, Volume 103, 2017, Pages 72-99, ISSN 0022-5096,

[3] Jian-Ying Wu, Jie-Feng Qiu, Vinh Phu Nguyen, Tushar Kanti Mandal, Luo-Jia Zhuang, Computational modeling of localized failure in solids: XFEM vs PF-CZM, Computer Methods in Applied Mechanics and Engineering, Volume 345, 2019, Pages 618-643, ISSN 0045-7825,

I have to think more about

Fri, 2021-04-02 02:45

In reply to fixed length scale

I have to think more about your model. It is not completely clear to me. CZM, by its definition, is not mesh sensitive as damage mechanics. Camacho and Ortiz (1996) proposed CZM similar to yours yet not diffused. What are the benefits of diffused CZM? The fact that you need extra strength constraint is a disadvantage typical of CZM. The whole idea of continuum damage mechanics is the possibility to completely describe failure and fracture by using constitutive equations only. That makes CDM advantageous as compared to cohesive surfaces, which require additional conditions of their insertion. Your diffused CZM requires fine meshes while the classical CZM does not... 


Thu, 2021-04-01 20:14

In reply to I don't disagree with your

I agree with you on the second point. Application of the AT1/2 models to Concrete or more generally, quasi-brittle solids (even the so-called brittle solids exhibit quasi-brittle behavior at smaller scale) might be inappropriate.

For the first point, just as the cohesive zone model applies to both brittle fracture with a "small" internal length scale and quasi-brittle one with a "larger one", it might be more helpful if such a counterpart exists in the phase-field framework.


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