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# Comments

### More details would be needed.

*In reply to Thermally induced residual stress*

More details would be needed. Type of material, process through which it is made and so on.

### Abaqus mailing list

*In reply to Modeling Soil around pipeline with stiffeners in abaqus*

Hello

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or from the ResearchGate discussion forum.

Good luck

Frank

### If you are interested in

*In reply to Abstract Submission to ICME Prize Extended to August 24. *

If you are interested in submitting, please request the extension from Prof. Wenbin Yu at wenbinyu@purdue.edu.

### Thank you Dr Kourousis for

*In reply to Crack Growth Resistance in Metallic Alloys: The Role of Isotropic Versus Kinematic Hardening*

Thank you Dr Kourousis for your comments.

Regarding your first question. We did not include the values of c_k and gamma_k because it is basically a curve-fitting. In fact, if you use a commercial finite element code like Abaqus what you provide is the uniaxial stress-strain curve (and the number of parameters, k=10), and Abaqus does the fitting for you. Thus, going from isotropic hardening to kinematic hardening just involves changing one line in the input file. Moreover, note that if you use other approaches, such as multilinear kinematic hardening (implemented in ANSYS since a few years ago and in Abaqus since 2017) you will get similar results in the crack growth problem. In any case, one can request the values of c_k and gamma_k, along with the fitting precision, so I have looked into my notes and the parameters used seem to be the following:

N=0.2 - c_1: 0.64945, gamma_1: 1.02E-04; c_2: 1.8295, gamma_2: 8.25E-04; c_3: 5.5242, gamma_3: 3.77E-03; c_4: 17.798, gamma_4: 1.61E-02; c_5: 60.82, gamma_5: 7.22E-02; c_6: 195.53, gamma_6: 0.32148; c_7: 652.78, gamma_7: 1.4174; c_8: 2182.2, gamma_8: 6.4444; c_9: 7391, gamma_9: 30.334; c_10: 23610, gamma_10: 173.42.

N=0.1 - c_1: 2.77E-02, gamma_1: 0; c_2: 0.21698, gamma_2: 4.62E-04; c_3: 0.89669, gamma_3: 2.99E-03; c_4: 3.5643, gamma_4: 1.47E-02; c_5: 15.397, gamma_5: 7.34E-02; c_6: 62.707, gamma_6: 0.36018; c_7: 263.63, gamma_7: 1.7468; c_8: 1072.1, gamma_8: 8.6006; c_9: 3986.5, gamma_9: 41.256; c_10: 12163, gamma_10: 220.63.

Regarding your second question. This automated fitting to the tensile part of the uniaxial stress-strain curve shows that, for 10 c_k and gamma_k, the kinematic hardening model matches the isotropic hardening model up to a stain of 2 with the largest difference being of 0.04%. We are dealing with monotonic/static loading, where the translation of the yield surface with crack advance is always neglected. What we show is that if you model crack propagation with a kinematic hardening model that matches the isotropic case in uniaxial tension, then significant differences arise in the crack growth resistance curves. In other words, one should not neglect anisotropic/kinematic hardening effects in monotonic/static loading.

Thank you

Emilio Martínez Pañeda

### Can you also explain this?

*In reply to Crack Growth Resistance in Metallic Alloys: The Role of Isotropic Versus Kinematic Hardening*

Can you also explain this? "The choice of n=10 brings the CAF model into alignment with (4) to within 0.04% for the range of true tensile strain 0<=e<=2.0"

In particular, why did you choose to capture the initial loading branch (tension) and not the subsequent unloading-reloading branches (compression-tension) of the hysteresis loops?

### Missing Parameters

*In reply to Crack Growth Resistance in Metallic Alloys: The Role of Isotropic Versus Kinematic Hardening*

Can you provide the values of c_k and gamma_k (10 parameters in total)? These are currently missing from the paper.

### Re: Cubic scaling in DFT...

*In reply to Re: Faster DFT calculations*

1. ``However, the use of multigrid does not change the cubic-scaling with respect to the number of atoms, which is a consequence of the underlying eigenproblem.''

Oh, I see.

2. ``[CheFSI's] performance is very weakly dependent on the spectral width of the matrix being diagonalized...''

Thanks for clarifying this part too, and indeed, for taking care to address all other issue I raised.

Best,

--Ajit

### Re: Faster DFT calculations

*In reply to Faster DFT calculations*

"You mention the cubic scaling with # of atoms, which implies the limitation of only a few hundred atoms. The first thing to strike me when I read it was this: how about multi-gridding?"

There have been efforts like the ones you referenced for developing multigrid preconditioning for the DFT problem, which can be used to reduce the prefactor associated with real-space DFT calculations. However, the use of multigrid does not change the cubic-scaling with respect to the number of atoms, which is a consequence of the underlying eigenproblem. Indeed, the scaling can be made linear by employing the nearsightedness principle, as discussed in my post. As is to be expected, the prefactor associated with linear-scaling approaches is significantly larger than the cubic-scaling approaches.

"So I was wondering whether your approach already makes use of it or what."

We do not utilize the multigrid preconditioning for our diagonalization based formulations and implementations (e.g. SPARC). Instead, we employ partial diagonalization based on CheFSI [28] whose performance is very weakly dependent on the spectral width of the matrix being diagonalized, therefore alleviating the need for preconditioning.

"Could you please share your thoughts on MG for DFT? Is it suitable? Does it work for the kind of (mechanics-related) problems you mention above? What are the constraints for using MG in DFT?"

Multigrid preconditioning can significantly reduce the prefactor associated with real-space DFT calculations. However, as mentioned above, it does not improve the scaling. Furthermore, methods like CheFSI alleviate the need for preconditioning, making them highly competitive. Finally, the complexity of multigrid in terms of formulation and implementation for eigenvalue problems (rather than the usual linear systems of equations) makes them less desirable.

[28] Zhou, Y., Saad, Y., Tiago, M.L. and Chelikowsky, J.R., 2006. Self-consistent-field calculations using Chebyshev-filtered subspace iteration. *Journal of Computational Physics*, *219*(1), pp.172-184.

### Re: DFT calculations for dislocations

*In reply to DFT calculations for dislocations*

"What is the simplest crystal defect for DFT calculations?"

In general, the simplest defect will be point defects, e.g., vacancy.

"Does it have to be a periodic arrangement of defects or it is possible to analyze a single defect?"

Traditionally, DFT approaches have employed the plane-wave basis (i.e., Fourier basis). Therefore, they are restricted to periodic boundary conditions, which translates to a periodic arrangement of defects. Using real-space methods like the one I described in my post (e.g. SPARC), it is possible to impose Dirichlet or periodic boundary conditions or a combination thereof. However, a number of questions remain, the main one being: what are the appropriate boundary conditions on the electronic structure quantities? (Recall that we are dealing with an eigenvalue problem). Indeed, an alternative to finding and applying such boundary conditions is to coarse-grain DFT [21,22].

"Are you aware of any DFT calculations for dislocations?"

Given their importance, there have been a number of efforts to study dislocations using DFT. Three broad classes of strategies that are adopted are: (i) Quadrupole or dipole method, e.g., [23,24], (ii) Development of new boundary conditions, e.g., [25,26], and (iii) Multiscale methods, e.g., [27]. Each of these approaches have their own limitations and strengths in terms of accuracy, efficiency, and the quantities they can calculate.

[23] Bigger, J.R.K., McInnes, D.A., Sutton, A.P., Payne, M.C., Stich, I., King-Smith, R.D., Bird, D.M. and Clarke, L.J., 1992. Atomic and electronic structures of the 90 partial dislocation in silicon. *Physical review letters*, *69*(15), p.2224.

[24] Dezerald, L., Proville, L., Ventelon, L., Willaime, F. and Rodney, D., 2015. First-principles prediction of kink-pair activation enthalpy on screw dislocations in bcc transition metals: V, Nb, Ta, Mo, W, and Fe. *Physical Review B*, *91*(9), p.094105.

[25] Woodward, C. and Rao, S.I., 2002. Flexible ab initio boundary conditions: Simulating isolated dislocations in bcc Mo and Ta. *Physical review letters*, *88*(21), p.216402.

[26] Yasi, J.A., Hector Jr, L.G. and Trinkle, D.R., 2010. First-principles data for solid-solution strengthening of magnesium: From geometry and chemistry to properties. *Acta Materialia*, *58*(17), pp.5704-5713.

[27] Lu, G., Tadmor, E.B. and Kaxiras, E., 2006. From electrons to finite elements: A concurrent multiscale approach for metals. *Physical Review B*, *73*(2), p.024108.

### Faster DFT calculations

*In reply to Journal Club for July 2018: Mechanics using Quantum Mechanics*

Dear Phanish,

I had read with interest this great description which you have written. (Very good condensation.) A thought had struck me right on the first read. However, something else (including travel) came up in the meanwhile. ... Anyway, I am glad that there still is some time left to discuss it...

OK. Refer to your very first paragraph. You mention the cubic scaling with # of atoms, which implies the limitation of only a few hundred atoms. The first thing to strike me when I read it was this: how about multi-gridding?

So I was wondering whether your approach already makes use of it or what. (Sorry, no time to go through the papers you list... So, just asking...)

However, I also did a rapid Google search today and found, e.g., this: http://homepages.uni-paderborn.de/wgs/Dpubl/pss_217_685.pdf and this: https://repository.lib.ncsu.edu/bitstream/handle/1840.2/203/Bernholc_200... . Both are c. 2000 papers. There must have been more studies and developments since then.

Could you please share your thoughts on MG for DFT? Is it suitable? Does it work for the kind of (mechanics-related) problems you mention above? What are the constraints for using MG in DFT? ... Would like to know your views... Thanks in advance.

Best,

--Ajit

### added bold entries

*In reply to PhD studentship at the University of Parma (in Parma, Italy) on modelling hydraulic Turbines*

added bold entries

### DFT calculations for dislocations

*In reply to Journal Club for July 2018: Mechanics using Quantum Mechanics*

Dear Phanish:

Thanks for the excellent discussion. You mention defects. What is the simplest crystal defect for DFT calculations? Does it have to be a periodic arrangement of defects or it is possible to analyze a single defect? Are you aware of any DFT calculations for dislocations? Thanks. Regards,Arash

### <p>position filled!</p>

### Great Work!

*In reply to Mechanics of spontaneously formed nanoblisters trapped by transferred 2D crystals*

Great Work!

### Dear Professor,

*In reply to UMAT wrote in C/C++*

Dear Professor,

Could you also send me the documents? If there is an example for the head of the subroutine, it will be more helpful. Thank you in advance!

Ni

### Abstract submission deadline extended

### deadline august 6th

*In reply to several phd positions at the Dept Mech Engineering Politecnico di BARI*

..but you can obtain the degree by Oct.31 if you are still in the process.

mc

### for details about phd application visit

*In reply to several phd positions at the Dept Mech Engineering Politecnico di BARI*

http://www.poliba.it/sites/default/files/dottorati/bando_34_ciclo_dottor...

Ph.D. in MECHANICAL ENGINEERING AND MANAGEMENT

do not hesitate to contact me at mciava @ poliba . it for any clarifications.

mc

### IWCONWEP

*In reply to Equivalent Conwep pressure in abaqus*

**Description: **Pressure loading due to an incident shock wave caused by an air explosion is calculated using the CONWEP model in Abaqus/Explicit. The new element field output variable IWCONWEP can now be requested on the element faces on which you apply this type of pressure load.

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