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# Comments

### Derivation of Griffith's Equation

*In reply to The Griffith Paper*

Prof. Suo

In your notes the condition of fixed grip has been assumed so that no work is done by the external force. This gives an expression for U. This is differentiated to find the critical stress σc. It is assumed that that the stress σ is constant. But in a fixed grip situation won't σ change as the crack grows?

### Is this job only for us

*In reply to Post-Doc Position in Experimental Impact Mechanics Available at Sandia National Laboratories*

Is this job only for us citizen? Thanks.

### Hi,

*In reply to Newton Raphson for FEM*

Hi,

I know the question is a bit old. I assume you have found the way out. In any case, to get the tangent tensor (1st derivative of the matrix), you would have to compute the 4th order tensor. Be clear with the tensor calculus before coding. I suggest you to check for some in-line matlab functions as well.

Regards

### Abaqus mailing list

Subscribe to and seek assistance from the

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Search the archive before posting.

For an intro to subroutines get the file

http://imechanica.org/files/Writing User Subroutines with ABAQUS.pdf

Good luck

Frank

### Thank you for your nice

*In reply to Strain gradient plasticity modeling of hydrogen diffusion to the crack tip*

Thank you for your nice comment. I look forward to reading your work on the topic.

### Regards, Ellla

### I have the same problem :(

*In reply to THE CRITICAL FRACTURE ENERGY erro using ABAQUS simulate fracturing*

Hello Hanrrycn,

My Ph.D. is very similar to this subject. I have some questions about how you solved this problem. First of all, I want to know how you applied initial stress condition ?I mean how did you calculate them?because they wrote subroutine SIGINI for that.

my second problem is that how to apply pore pressure Boundary condition and I see you have none. However, in the corresponding Abaqus manual, they defined pore pressure which is very confusing for me. here I copy and paste .

*Boundary,user

**_PickedSet5, 8, 8, 1

TOP, 8, 8, 1

BOT, 8, 8, 1

### I have the same problem :(

*In reply to THE CRITICAL FRACTURE ENERGY erro using ABAQUS simulate fracturing*

Hello Hanrrycn,

My Ph.D. is very similar to this subject. I have some questions about how you solved this problem. First of all, I want to know how you applied initial stress condition ?I mean how did you calculate them?because they wrote subroutine SIGINI for that.

my second problem is that how to apply pore pressure Boundary condition and I see you have none. However, in the corresponding Abaqus manual, they defined pore pressure which is very confusing for me. here I copy and paste .

*Boundary,user

**_PickedSet5, 8, 8, 1

TOP, 8, 8, 1

BOT, 8, 8, 1

### I have the same problem :(

*In reply to THE CRITICAL FRACTURE ENERGY erro using ABAQUS simulate fracturing*

Hello Hanrrycn,

My Ph.D. is very similar to this subject. I have some questions about how you solved this problem. First of all, I want to know how you applied initial stress condition ?I mean how did you calculate them?because they wrote subroutine SIGINI for that.

my second problem is that how to apply pore pressure Boundary condition and I see you have none. However, in the corresponding Abaqus manual, they defined pore pressure which is very confusing for me. here I copy and paste .

*Boundary,user

**_PickedSet5, 8, 8, 1

TOP, 8, 8, 1

BOT, 8, 8, 1

### Thanks again!

*In reply to Matt, congratulations on your*

Thanks for your response! I completely agree with you that a better physical explanation of the mechanism of fracture of these materials is vital. Perhaps we can do some experiments to investigate microstructural features associated with the fracture process and in turn shine some light on differences among other experimental observations at the macro-level.

### Electrochemically driven mechanical energy harvesting

*In reply to Hui, thank you very much for*

Hi Shuman,

In our Nature Communication paper, we used nano-thick thin-film Si as the electrodes. Because of the nanoscale size, surface diffusion is domaint (and fast). Ge is certainly better; but more expensive. From a cost-effectiveness point of view, we shall seek for different forms of Si (such as nano porous Si) to improve the rate capability of the device, while make it potentially commercializable.

### SEI formation

*In reply to Journal Club Theme of July 2016: Mechanics of Large-Volume-Change Materials for Rechargeable Batteries*

Hi Shuman,

A very nice review on the experimental side of the mechanics of anodes for lithium ion batteries. I am pround to see that our mechanicians have done a great job in evovling the field and helping electrochemists understand the electrochemical behavior of the large-volume-change anode materials.

Two borthering, but valid questions remain. One is the SEI formation, the other is the pore formation (ubiquitous in almost all the anode materials) during delithiation. The first question is obvious but our mechanicians rarely touch it (constantly complained by electrochemists in our proposals). The second question is less obvious, but we often see that the lithiation behavior (for exmaple, amorphous Si) is very different during the first and subsequent cycles, indicating its importance. Can our experimentalists help solving these problems before moving to other battery forms (such as Li-air) ?

### Matt, congratulations on your

*In reply to Experimental measurements of fracture energy*

Matt, congratulations on your new faculty position! It’s indeed great to see we have found similar results from very different approaches. You have made some very good points to explain the slight difference between our observations at elevated Li concentrations. I agree that the loading rate plays an important role in the fracture properties of lithiated electrode materials. The lithiated materials in our TEM and nanoindentation experiments were mechanically loaded within a few minutes, while your samples were loaded at a much lower rate using electrochemical lithiation. Another possible cause I have thought about is the difference in the stress states between our samples. Your electrode films were subjected to biaxial stress during fracture testing. For our TEM and nanoindentation samples, the stress state was close to uniaxial state. In conventional fracture mechanics of metals, the stress state at a crack tip is known to have a great influence on the fracture toughness due to its effect on microvoid nucleation and coalescence. Similarly, lithiated materials may exhibits some kind of stress-state dependence but its physical origin may differ from metallic fracture and warrants further investigation.

### Hui, thank you very much for

*In reply to Lithiation mechanics of high-capacity anode materials*

Hui, thank you very much for your comprehensive review. In your Nano Letters paper, you showed that mechanical stress could induce symmetry breaking of lithiation in germanium nanowires. In your more recent Nature Communications paper, it was demonstrated that the same stress-diffusion coupling occurs in lithiated silicon and could be harnessed for mechanical energy harvesting. This is a very creative and stimulating idea. I just wondered if you have ever considered or tried using germanium for making energe harvesting devices. Germanium has much higher Li diffusivity than silicon. Intuitively, it may exhibt greater stress-duffusion coupling and therefore offer higher envery harvesting effeciency. Any thought?

### Thank You.

*In reply to Postdoctoral Research Position at University of Maryland, College Park, MD, USA*

Thank you all for your interest in the position and for submitting your application. The final candidates for this position have been selected.

### UMAT error

*In reply to Remarks on UMAT for plane stress problem*

Mr. Zhang,

Your post has bee very informative. However after trying tho implement them, Abaqus throws an error at me.

What I did is calculate the F33 by imposing the Sigma33 = 0 constraint and calculate F33 iteratively from this equation (non-linear root finding method). Then I used this F33 for finding the stress value returned to Abaqus.

For the material Jacobian, first I determined the 6x6 matrix first and reduce it to the 3x3 matrix by substituting for D3 in Tau1, Tau2 and Tau4 expressions and taking the coefficients of the D1, D2 and D3 as the components of the 3x3 material jacobian matrix.

(here F represents the deformation gradient, Tau represents the variation in Kirchoff Stress and D represents the rate of deformation)

However when I use this UMAT with the CPS8R element, Abaqus throws up the following error:

"ERROR in job messaging system: Error in connection to analysis.

Error in job 2D-CPS8R-TrialUMAT: Abaqus/Standard Analysis exited with an error - Please see the message file for possible error messages if the file exists. Job 2D-CPS8R-TrialUMAT aborted due to errors."

For debugging the UMAT I have opened a "debug.log" file in the UMAT and have given write out of variables to this debug log file. However I cannot find the debug.log file in the job directory which might mean that Abaqus is not reading the UMAT file. I have already checked the link with Fortran compiler. The "Data Check" completes successfully but on submitting the job the above error shows up.

Could you please give any pointers on what I am doing wrong?

I would have attached the UMAT and inp but could not find how!

### The J-integral for multiple cracks

*In reply to Per, thanks for raising this*

Dear Bent,

First I want to say again that I enjoyed reading your paper and the struggle you had with the secondary crack and the vanishing contribution to the J-integral.

The J-integral computes the energy release rate of whatever is enclosed if it/they should move a unit increment in the x-direction.

In your case it means, that the primary crack tip and the right secondary crack tip, require energy for growth, i.e., the cohesive energy density times the amount of crack growth. The left secondary crack tip is healing which releases the same amount of energy as is consumed at the right crack tip.

The nice parts are that 1) nothing happens to the stress distribution in the region with the crack tips and, 2) the work done by the external bending moment acting at the beam end is easily assessed by recognising that the only essential thing that happened is that the beam got extended with the short advance of all crack tips in the x-direction. All this is nicely captured by the J-integral as your analysis shows. The contribution from the secondary crack vanishes which is the expected result, though.

According to your observation the secondary crack grows at both ends. The assumption that one of the cohesive zones does not open will result in stress singularity and the contribution to the J-integral via a loop around the crack tip will probably be more or less the same negative value as before. As earlier the J-integral is still giving the energy released for the three crack tips moving a unit length in the x-direction.

As I see it, the result improves when you remove the contribution from the crack tip that is growing in the negative x-direction, but still this is not fully correct. If all crack tips are growing, the energy release rates are possibly close to the cohesive energy densities times the respective crack growth rates that you observed. The reason why I suggest this is that it will be correct for small scale bridging zones. How good it is with the large process zones that you have, I don’t know.

Another obstacle is the connection to the result for the remote path J-integral that also would give the energy released for all crack tips moving the same short unit distance in the x-direction. The calculation is based on bending of a beam that becomes longer because of the crowing crack. The ”crack growth rate” becomes essential. Should it be taken as the average measured in the x-direction even though all cracks are not moving in the positive x-direction, or maybe the average absolute value, or something else?

Per

### Ting, thanks for bringing up

*In reply to Mechanics of Li anode*

Ting, thanks for bringing up this interesting subject. Lithium metal as an anode material has the highest capacity (3.86Ah/g) and has been widely used in commercial primary (i.e., non-rechargeable) lithium batteries. However, the use of lithium in rechargeable lithium-ion batteries has mainly been hindered by dendrite growth on repeated cycling. Some computational models have recently been developed to simulate this growth process. To suppress dendrite growth, many strategies have been proposed in the past. These include coating lithium anode surfaces, forming composite Li structures, applying external pressure, and replacing conventional liquid electrolytes with polymer- or ceramic-based solid electrolytes. It is undisputable that mechanics is in a key position to implement and mainstream these methods, and it’s up to us to unlock its full potential!

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