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# Comments

### Inquiry about your available PHD positions

*In reply to PhD studentship at URV, Tarragona, Spain*

<p>Dar Prof. Huera,</p>

<p>My research fields exactly coincides with your research areas. I sent an email to you yesterday with my CV attached. I will appreciate you if you take a look at my CV.</p>

<p>Thanks in advance</p>

<p>Morteza Alinia</p>

<p>Email: <a href="mailto:m.alinia@me.iut.ac.ir">m.alinia@me.iut.ac.ir</a></p>

<p> </p>

### hello Mr Jahanshahi

*In reply to Displacement Controlled Analysis*

hello Mr Jahanshahi

thank you so much for your attention.

I will do what you said.

M.Jafarzadeh

### hello peto24ap

*In reply to Geometric nonlinearity*

hello peto24ap

Why do you use line 4 method for computing internal force? I think this is the problem. Use ordinary method for internal force, Just like the method introduced in " introduction to finite elements in engineering" ,by chandrupatla or every other fnite element book, to make your internal force vector.

look for this article "COMPOSITE MATERIALS IN COMPRESSION " by Jens Lycke Wind, In this thechnical report you can find an algorithm for Newton raphson.

I used it before for load base problem but i could not write a code for material nonlinearity which is under displacement BC, and displacement control.

Ask me if there is some thing to ask, our ways are similar. maybe we can help each other in the modeling

M.J

### Hi, There are several arc

*In reply to arc length in delamination*

Hi, There are several arc-length methods that could be used. But depending on the level of non-linearity, they may or may not be able to trace snap-back exactly.

Geometrical nonlinearity simple arc-length method should be sufficient. But in case of severe strain localization, you would need a method like the one suggested by

Crisfield arc-length method. Try this one, incase this one does not work, I may have other suggestions.

Best

### Displacement Controlled Analysis

*In reply to displacement control method *

Dear Mr. Jafarzadeh,

I already have answered your question. The answer lies in equation (2) above. In the fisrt iteration of each load step (which is displacement controlled) you apply an incremental displacement. Of course your stiffness matrix should be comouted in each iteration due to material nonlinerity. In subsequent iterations the second term on the right hand side of equation (2) is set to zero and iterations continue to equilibrate out of balance force. The iterative procedure is exactly similar to force-controlled except for equation (20). If you pay a good attention to what I siad you should be able to proceed without any problem.

Good Luck

### displacement control method

*In reply to Displacement Controlled Analysis*

hello Mr Jahanshahi

thank you for your quick answer

I know how to find reaction forces for the case but my problem is how to use displacement control method for displacement BC case, in which the stiffness matrix in each increment and iteration change. In displacement BC by changing stiffness matrix the total force changes too. I should apply a unique force for each increment to use it in all the iteration.

M.Jafarzadeh

### Displacement Controlled Analysis

*In reply to N-R method*

Consider the following partitioned matrix equation (sorry if I could not show it clearly):

|**K**nn ¦ **K**nu||**u**n| |**R**|

|.......¦.......||....| = |...| (1)

|**K**un ¦ **K**uu||**u**u| |**F**|

In this equation *u**n* is the vector of specified (and thus known) displacements. This is the specified displacement at certain degrees of freedom in displacement controlled analysis. ** R** is the vector of corresponding reactions at these degrees of freedom. The vector

*u**u*is the vector of unknown displacements at other degrees of freedom where no displacement boundary condition is specified.

**is the vector of nodal forces at these latter degrees of freedom. From the second row of this equation we can write:**

*F*[**K**uu][**u**u]=[**F**]-[**K**un][**u**n] (2)

which is the equation that should be solved in displacement controlled analysis. Based on this equation, the vector of forces at unconstrained degrees of freedom should be modified by the second term on the right hand side of equation (2). The rest of the analysis is exactly the same as force controlled analysis. Having calculated *u**u* from preceding equation, the vector of reactions at constrained degrees of freedom can be calculated from the first row of equation (1) as

[**R**]=[**K**nn][**u**n]+[**K**nu][**u**u] (3)

For more information you can refer to page 187 of the following reference:

K.J. Bathe, *Finite Element Procedures*, Prentice-Hall, 1996.

### Helpful tips really nice

### D&DT course - Part II on Fatigue & Damage Tolerance

*In reply to Course on Design Principles, Fatigue & Damage Tolerance for Aeronautical Engineers*

Dear iMechanicians,

Part I of the D&DT courese on Design Principles for Aeronautical Engineers starts just after this weekend. Those, who would be more interested in Fatigue & Damage Tolerance topics, please note this part of the course will be held from November 11 till November 13. The applications, if possible, should be filled in till October 27. If interested, see the details on www.pragtic.com/DDT.php.

Best regards

Jan

### N-R method

*In reply to Nonlinear Algorithms*

Hello Mr Jahanshahi

I wrote a code by N-R method for my problem (a double cantilever beam which has interface elements between two layer for simulating delamination ), every thing was good, I saw the softening of the material, but there was some problem.

For verifying my answers, the Reaction-displacement of the total system should be plotted,for this reason i should impose displacement boundary condition instead of force.

As you know in the material nonlinearity problem the stiffness matrix (D and after that K) will change in every increment and iteration corresponding to displacement (in the geometrical nonlinearity the displacement changes alter the geometry and after that the total stiffness matrix changes). by changing in the stiffness matrix also the force value will change , because of displacement BC formulation in finite element method.

but in the N-R method the at the beginnig a load apply to the system and then in each increment 1 part of it will impose. In my case the force change with K.

now here is my question: Can i use N-R method for displacement BC problem or I must use the displacement control method?

I try displacement control before but I didnt succeed. In this method I have same problems. In displacement control method a first force (not displacement) will introduce, and then a part of force impose in increments. But the base is displacement change. Also In this method the K matrix changes and it is main problem.

I want a method appropriate for displacement BC problems.

Would you please help me in this topic too?

M.Jafarazadeh

### You can post your specific

*In reply to could someone tell what should I do to run Abaqus job in High Performance Computing (HPC) systems?*

You can post your specific question here, https://swym.3ds.com/#community:73/iquestions

### Thanks for your help! A

*In reply to This problemlooks like*

Thanks for your help! A follow up question is that when import a model to Solidworks or AutoCAD, Abaqus can export multiple file extension, such as ACIS (.sat), IGES (.igs)and STEP (.stp). Do you know which is better from 3D reconstruction. By the way, our model is a cylindrical shell.

### Postdoc looking for a job

*In reply to Research Associate/ Postdoctoral Research Associate position in Magnesium Alloy Development*

الأخ المحترم الدكتور بلال منصور

السلام عليكم ورحمة الله وبركاته

أود الاستفسار عن فرصة العمل المذكورة اعلاه إذا لا تزال متوفرة أم لا؟

أنا ابحث عن فرصة عمل في مجال دراسة سبائك الماغنيسيوم وطرق تحسين خواص التآكل بها.

أنا خريج جامعة مانشستر لهذه السنة ولدي درجة دكتوراة في هذا المجال وكذلك درجة ماجستير في علوم المواد والتآكل.

ساقوم بتزويدكم بسيرتي الذاتية في حال كانت هذه الوظيفة مازالت شاغرة.

تقبلوا تحياتي مع جزيل الشكر

والسلام عليكم ورحمة الله وبركاته

د. أحمد الشيخي

### These are a number of research papers and textbooks

*In reply to These are a number of research papers and textbooks*

yes, These are a number of research papers and textbooks by Prof. W. Noll. I suppose they definitely deserve to be here.

### This problemlooks like

*In reply to 3D Printing of an imperfect cylindrical shell*

This problemlooks like surface reconstruction problem. I have heard of plugin in solid works "Scanto3D". See

https://www.youtube.com/watch?v=GrVZR1cldu4

This plugin can be activated if it does not exists.

There are other packages which can generate surface from point cloud:

1. Resurf plugin in Rhinoceros : fits NURBS surface to point clouds.

2. Mesh lab : using "voronoi filtering" algorithm generates facets on the given point cloud.

### Hello Mr Jahanshahi

*In reply to Nonlinear Algorithms*

Hello Mr Jahanshahi

Thank you for your attention.

I will read the Owen book certainly and I will apply the Newton Raphson in my code too.

m.jafarzadeh

### hello Mr Sreenivas

*In reply to Hello
*

hello Mr Sreenivas

Today I saw your comment about the book "Development and Application of the FEM based on MATLAB", but the link doesnt work any more.

I tried to find it by google search,but there wasnt any thing.

Would you please guide me to find this book.

by the way, I'm trying to simulate a material nonlinearity problem, Do you know some thing that can help me in this way?

thanks

m.j

### Nonlinear Algorithms

*In reply to displacement control for material nonlinearity problem*

Hello m.j,

1. You have to be careful about arc length method. If lambda is greater than 1 then the results obtained by arc length method might not be correct. Using full Newton-Raphson method with reasonable step size can be a good substitute if you are not sure of what you are doing.

2. You can consider two tolerances for your algorithm for example 10e-10 and 10e-5. You can enforce the first tolerance in your iterations. If the tolerance obtained after the total iterations are exhausted is greater than the first tolerance but less than the second your results are fairly accurate within the second tolerance and you can move to the next iteration. Otherwise your results are not accurate enough and you have to cease the iterations.

3. You can consult the following book. It is full of algorithms and flow charts which suit your needs:

Computational Methods in Plasticity: Theory and Applications, EA de Souza Neto, D Peric and DRJ Owen, John Wiley & Sons, 2008.

Mohsen

### hi

### Dear Prof. Brocks

*In reply to The Configurational Force Approach in Elasto-Plastic Fracture*

Dear Prof. Brocks

I am the first author of the paper you commented on. I appreciate that you decided to learn and to study the material force approach after our talk at the IWPMEO workshop in Antalya, Turkey, 2013. You told me that you were not aware of this method. I believe that you are still missing some parts of the concept.

First of all, thank you for your interest in our paper. I also appreciate that you expected a new theory from our review paper but it is obvious from the title that it is indeed a review paper in order to evaluate the method. However, when we started to implement and to study the material force approach in small strain plasticity, the main concern was which energy contribution should be considered to derive the momentum balance equation in the material space. It had to be investigated which derivation yields the crack driving force or rather the energy release rate available for crack propagation and whether it is possible to separate them by this approach or not. Although I found some authors using different energy contributions, I could not find really a clear and comprehensive study taking all the resulting terms into account in case of plasticity neither in papers on the J-integral nor in papers on the material force method in combination with numerical studies and comparisons (if you know one, please inform me).

Then, I began to study the formulation by using different energy terms. I found that in the traditional J-integral, which is commonly used in commercial software, the total stored energy in the bulk and dissipated energy are used in the Eshelby part of the equation (which is Rice’s J-integral in this case) and the so-called material body forces are ignored where the calculation of the gradient terms is required. Thus, in the paper, we showed that when the total energy in the bulk is considered as the energy available in order to obtain the crack driving force as it is in Rice’s J-integral, there are still gradient terms, which need to be included to formulation (or material body forces). However, in software, people simply ignore those terms since they vanish when the system is under monotonic loading. Furthermore, we derived material forces for plasticity from three different energy contributions in Section 5.3 of our paper:

I) Energy in the elastic spring

II) Energy in the elastic and hardening spring (the total stored energy in the bulk)

III) Energy in the elastic and hardening spring and sliding frictional element (the total stored energy in the bulk and dissipated energy by plasticity)

and compared the results for the close field and for the far field integration to an experimental study. I believe that you missed this part in the paper and you made the criticism that it was just a software implementation. Besides, even if there is a paper which already explains the full formulation with additional terms for the different energy contributions as I explained above, numerical challenges still remain to calculate the gradient of the terms in the discretizated continuum. I believe this part of the approach still needs some further study.

The path dependency study in the paper is a kind of prove of the equilibrium of the material momentum balance equation. In other words, the system must satisfy the balance equation and the path independency is the result of vanishing of nodal material forces in the part of the body, where singularity (or inhomogeneity) does not exist (in far field). Therefore, path dependency study is a verification of the concept of the material momentum balance and a verification of the implementation especially in the case that the calculation of the gradient terms is required in the formulation.

Therefore, we made a path dependency study on the material force and the Rice’s J-integral. As a result, we did not get path dependency for the material force approach even in the fracture process zone (in plastic regime) which has not been illustrated numerically in a comparative study yet according to my knowledge. As you know, the limitations of the J-integral in plasticity have always been a question. Therefore, even though it is a review paper, I believe that we presented something new by using various energy terms and showing the results numerically. Moreover, another contribution of the paper is to validate the computations against published test data, which is not available according to our knowledge. The reviewers and editor agreed with us and decided to publish the work.

To your other questions.

*“**the authors start with a display of fireworks introducing the general nonlinear kinematics of large deformations which can be found in every respective textbook. In the end, this impressing framework is simmered down again to “**small strain elasto-plasticity and hyperelasto-plasticity**”, whatever “**hyperelasto-plasticity”** ** is supposed to mean.**”*

What you consider as "fireworks", are just the required fundamentals of the general description of the plasticity concept and it must be introduced to clarify the notation and to derive the momentum balance equation in both spaces. This procedure is standard in deriving thoroughly results in continuum mechanics. However, I believe that it is not possible to claim that Eq. (23) in the paper, which is obtained from the gradient of the Helmholtz energy function, is a momentum balance equation in material space, unless we describe the difference between material (un-deformed) space and spatial (deformed) space and the mappings between them. For this point, I would like to draw your attention as well to the following papers

*Steinmann, P. (2000). International Journal of Solids and Structures 37, 7371–7391.*

*Steinmann et al. (2001). International Journal of Solids and Structures 38, 5509–5526.*

*Maugin et al. (1992). Acta Mechanica 94, 1–28.*

*Menzel et al. (2004). Computer Methods in Applied Mechanics and Engineering 193, 5411–5428.*

*Naeser et al. (2007). Computational Mechanics 40, 1005–1013. *

By the way, “*geometrically nonlinear*“ stands for a geometrically exact description without restrictions which means that the theory is not reduced to small strains or any type of simplifying assumption. I believe it is clear to the readers. Moreover, the term hyperelasto-plasticity is not used by us for the first time. It is a standard terminology in continuum mechanics. You can find more information on it at

http://scholar.google.com/scholar?hl=tr&as_sdt=0,5&q=hyper+elasto+plastic .

* *

Your other question:

*“So where are the problem and its solution after all?*

Problem:

What is the main difference between Rice’s J-integral , Kishimoto’s J-integral and the material force approach in plasticity and what is the role of the different energy contributions in material force and material body forces?

Answer:

The main differences are the energy contributions and additional terms, which we call material body forces. It seems that all three cases, that we studied, give the equivalent of the crack driving force for monotonic loading with the correction terms in far field calculation and they are path independent. For further studies, one may study arbitrary loading cases.

Your other question:

*“Can “material forces” be calculated by the finite element method - who doubts? Is the implementation of this concept in a commercial FE code a major scientific achievement - who knows?”*

Answer:

As I mentioned that although it is a review paper to show how people can use the approach and interpret the difference with the classical J-Integral, it gives a further study on energy contributions to clarify the difference between the methods by numerical studies. Does it solve all the questions on the approach? Of course not, but I believe that it is a step forward. Moreover, I do not know from which part of the paper you came to the conclusion that deformation plasticity is used in our study but we indeed used incremental plasticity. If we used deformation plasticity then material body forces would vanish which has already been shown in the following paper

* Simha et al. Journal of the Mechanics and Physics of Solids 56 (2008) 2876-2895, *

which I definitely recommend you to read.

Last but not least, I am really surprised about your style to comment on a scientific work. You could have approached us directly (email is given in the paper) in order to have an open and honest scientific discussion. Due to the fact that it is not the case, we just can speculate on your motivation putting these comments somewhere in the internet without any information given to us.

Regards,

Kaan Ozenc

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