I have two questions, that I am still confused on. Hopefully you can answer. 17:38 First, why did you not connect node 3 to anything? Why was N4 and N1 used instead of N3 and N2. Second, Lets assume you are applying a uniform displacement in the Z-direction that starts at NC and goes to ND. what corner/retained nodes would I use to connect my internal nodes?
Hello @Chase, thanks for the comment. I will attempt to answer. 1. Node 3 is called a slave node because, as a consequence of how the kinematic equations are defined, the node 3 adopts the degrees of freedom of nodes 2 and nodes 4 depending on the loading type. So, it has to be a slave node, and hence is not included. 2. The deformation along the Z-direction is slightly different. I wrote about this in the paper: doi.org/10.1016/j.commatsci.2012.12.036. If you read through it, you will see how I dealt with loading in the Z-axis, just a light change to the formulation already discussed in this video but certainly do-able.
Your videos are very good. Thank you. I appreciate the way you have to present and explain the topics. Definitively your videos are between the bests in abaqus explanation. Please continue creating more videos.
This video is very helpful. Eagerly Waiting for next two videos . Thanks for uploading this . This is the only video of PBC on TH-cam to describe it in such a nice manner.
Thank you DR. Okereke for the video of PBC, I hope you can publish some videos about the detailed PBC settings or whole simulations of woven fabric under tension
Thank you very much for your videos, Dr Okereke! They are all very helpful! It would be very interesting to learn how to apply PBCs on non-periodic meshes!
Hello @Athina, thanks for your interest in the channel. I am certainly interested in non-periodic meshes and have published about it which you can read here: doi.org/10.1016/j.compstruct.2016.10.114. I will make a series of videos about this in future. Please keep watching this space.
@@MichaelOkereke Thank you for your reply, Dr Okereke! I have read your work and I am in the process of altering my Periodic boundary conditions code by adding interpolations, as it is needed in my PhD project. Your publication has been very useful to understanding the concept! I will be checking your page for more videos!
Excellent video with high quality! I am quite interested in set a period boundary condition for non-period mesh. Could you please make one? Appreciate that!
Hello Ahmed, it is really a good question you ask here. I have done some modelling in the past with mixed BCs and so will try and do a demonstrative video about this.
Very interesting video to understand the Periodic Boundary Condition. But I would like to understand the difference between the representative volume element (RVE) and studying a normal specimen as the simulation of lab experiments and also the difference RVE and X-symmetry or Y-symmetry sections. Thanks in advance
Hi John, thanks for your interest in the channel. Representative volume elements are virtual domains that can be used as a substitute for the normal specimen. It is expected to give results that are comparable to normal experiments. Where you are finding it difficult to undertake the simulation of the normal specimen, then an RVE will be cheaper on computational time and can still give you good results. On your second question on RVE, X- and Y-symmetry sections, these are related. The X- and Y-symmetry is often used when identifying an RVE for a material. They are not the same but if you are looking to isolate an appropriate RVE for a physical domain, it is quite normal and common to consider the use of the X- and Y-symmetry of the material/domain to help you.
@@MichaelOkereke Thanks for your explanations but I have to use the Periodic Boundary Condition (PBC) whenever I modelling RVE or I can use the normal boundary conditions like fixed, hinge, roller too. If so, I would like to know when shall I use PBC, I mean how can I choose to use PBC or normal boundary conditions. Thanks in advance
Thank you for the video! I just wondering is is possible to apply PBC in a macro-scale model while we're intersting in discretizing full-scale model into smaller finite periodic model? Also, quite found a few resource in YT showing PBC application with the thermal analysis. Appreciate if you could emphasize on that!
Hi, Dr, Michael. Thanks very much for your video. I am recently researching helical structures, which also use PBC. However, that is more complicated because the canonical equation used inside is nonlinear and sometimes has a displacement coefficient. Therefore, I have to use the user-defined MPC inside ABAQUS, which I think is not so easy to implement and I still have some confusion about this subroutine. Could you please take a video and share with us some experience?
Hello Pan, thanks for the query. It does sound you are dealing with a really challenging task. If you can, share a paper about your problem and I can see if I'd better understand it. I have not used MPCs for applying PBCs but like you said it all depends on the canonical equations. I discussed this extensively in my FE book. If you have it look at the section about canonical equations and boundary conditions, it might help. I do need further information before I can consider it for a future video request. Cheers.
Hello Dr Okereke, I really learnt a lot on this video. I am definitely subscribing to the channel. I am not an ABAQUS user, I have been using COMSOL for modelling and simulation so I couldn't implement the ideas in the video. Regardless of this, I learnt a lot from the explanation. Do you use COMSOL? If yes, can you do a lecture on using Periodic flow conditions in Fluid Mechanics using COMSOL? Thank you.
Hello @Oluwaseyi Ayeni, thanks for the comment and am glad you found the videos helpful. I do not have much experience with COMSOl and so unable to help with Periodic Flow Conditions in Fluid Mechanics. Good luck with the research.
Hi, this is very interesting and well explained video. i have some question outside from this topic. how to analyze nonlinear geometrical behaviour of a 3d truss under externally excited harmonic force. how to determine their displacement and velocity w.r.t time for time domain and frequency domain analysis. another question how to select initial condition for dynamic problem. pls response my query.
Great video! Would the same concepts presented apply to FEM for Electromagnetics (i.e. Electric field)? Also, is there any special consideration for when there are multiple materials?
Hello @Jake, I believe this will apply also even for our electromagnetics field, depending on what type of field you are using. The method shown here works on Dirichlet-type boundary conditions, in which case, you specify define (constant) values at nodes at a given time-step during the simulation. In our case, if you can specify definite electric field to nodes in the boundary, then this method should work. However, it your electric field is a Neumann type boundary condition (in which case, it is not a predefined value but a traction, concentration, flux term), then this will not work. You really need to give it a go by modelling your problem and running the software on it to see if it generates a PBC-enabled RVE which you subsequently run to see what the results will be like. Good luck!
Hello @Johnson, I did not miss N3 deliberately. It is a slave node and inherits the deformation of other nodes, through the specified kinematic equation. I had provided further explanations in other comments on this video, so look at other comments and see my explanation.
Hello @Johnson, you are right, the developer (Dr Sadik Omirey) of EasyPBC is definitely an academic. While making this video, the reference to TH-camr was what came first into my mind but I do acknowledge that Dr Omairey is an academic as well as a TH-camr, just like myself.
When picking retained nodes that will be coupled with the internal nodes, those retained nodes have to be the ones that are influencing deformation on the entire system?
Hello @Chase, the retained nodes are essentially the nodes at the corners N1, N2, N3 and N4. However, N3 is a slave node, so unnecessary. YOu may like to look at this video where I explained more about applying, uniaxial, shear and combined loading using the retained nodes: th-cam.com/video/CqxdL0X8qec/w-d-xo.html . Let me know if you have any more questions.
Hello, Dr.Michael. I have another question. What if I want to give both uniaxial deformation and shear deformation on a RVE model , can I make it possible? I mean , how can I deal with this situation? I am really confused.
Very helpful tutorial video. Thanks for your sharing. I read your book and wonder if you can do the video on how to apply periodic boundary conditions to non-periodic mesh as you mentioned in your book and paper. Can I contact you?
Dear K M, thanks for your interest in the channel. I have the suggestion as part of my plan for the future. Keep watching. If you want to get in touch with me, you can join my CM Videos Insider Group using this link: cmvideos.ck.page/16a99bd0e3. You will check your mail to confirm subscription and then you can reach out to me as a CM Videos Insider.
Hello, thanks for the query. I am using a particular method in generating the PBC response which requires specifying a Dirichlet BC e.g. displacement at a retained/corner nodes. Since the RVE has kinematical constraints enforced using the *EQUATION command in ABAQUS, any movement at a corner nodes will cascade down the material (periodically) leading to the expected behaviour. I know some other authors use strain tensor (which they introduce into the model), but this is not how I do it. It is also a valid approach. I am not sure what you mean by solving the micromechanical problem with an iterative calculations, sorry!
@@MichaelOkereke hi, thanks for the answer.. my question go on the direction of plastic deformation but is not the case. About your answer, i have a question.. why PBC requires dirichled bc?
@@MichaelOkereke Hi, thanks for the answer.. my question are about non-linear and path dependent, but is not the case.. but i have another question.. why did you use Dirichlet BC?? where can i find literature about that and.. what is the model with strain tensor?? thanks
PBCs in the way I use require that you specify a displacement at a node hence the Dirichlet approach. It is only the displacement at one node that is Dirichlet. The other nodes are imposed with PBCs.
There are so much literature on PBCs but this was one that was particularly helpful when I was learning about this: 1. Kuznetsova paper: link.springer.com/article/10.1007/s004660000212 and 2. My paper: doi.org/10.1016/j.commatsci.2012.12.036 Hopefully these will help you.
@@MichaelOkereke Thank you! Do you mean U10y and U4y are pointing in the negative Y direction together? Also, U5y and U9y are pointing in the negative Y direction together?
Hello Chirag, thanks for your interest in the channel. If you want to contact me directly to discuss your project challenges, then please send an email directly to: michael.okereke@cmvideos.org.
It is a bit more complicated. When N2 moves by delta_x and N1 is constrained (fixed) then UN2=UN1 cannot be true. Actually UN2-UN1=delta_x not zero. Similarly UNB-UNA=delta_x etc. I guess this method does not allow to prescribe effective stress load on the edges, or does it?
Hello Robert, thanks for your comment. It is indeed complicated, the whole PBC stuff. I wanted to make some clarifications to your comments. First, N1, N2, N3 and N4 are called constrained nodes, so they are not prescribed with periodic boundary conditions. I use them to apply a required loading type to the model. So, when you say if UN1 is fixed say in the x-direction, that means the displacement there is zero. However, when UN2 is imposed with a delta_x load, then UN2 will have a dispalcement of UN2 = delta_x. As a consequence too, UN2 - UN1 = delta_x, as you rightly posited. However, at the onset of the model, without delta_x imposed on the system, UN1 = UN2 or in other words, UN1 - UN2 = 0, but when there is an imposed load, then the zero is replaced with delta_x. I believe you got this correctly. However, your second comment on UNB - UNA = delta_x is not necessarily true. This is because those are internal nodes that will not automatically take the value of delta_x. The only way they will take that value is when you kinematically link N1-N2 to NA-NB which is the equation I described as: UN1 - UN2 = UNA - UNB. If the system is homogeneous without any microstructural heterogeneity, then automatically, UN1 - UN2 = delta_x and then your comment is correct. However, as we are looking at heterogeneous systems, it is better to use the UNA - UNB nodal values as you travel along the edges (considering the internal nodes). In some instances, those nodal values may even result into negative values depending on the environment of the microstructural constituent of the RVE. I believe we are saying the same things but your comment relates for a special case where the domain is heterogeneous in which case the edge will deform uniformly (as if you imposed a dirichlet boundary condition to it). On the last comment around prescribing effective stress load on the edges, I am not sure I understand that. I know there is another PBC method where you do not explicitly impose delta_x to the edges. The other method is the strain tensor method, where you will apply a strain field to the domain using a virtual node, which is kinematically linked to a part of the model. The method uses the strain field to multiply the set of edge dimensions, which will again result into a set of displacements [delta_x delta_y delta_xy] and the like. In this case, the user will focus on the expected strain in the model as an input. The stress will result after the FEA simulation. I do not know of a case where effective stress is imposed as an input to the model. Please point me to any literature that deals with PBC in FEA like that. Thanks for your comments and I appreciate you thoughts.
Is it necessary to constrain the nodes on the edges and corners? If we only constrain the corresponding nodes on the edges and then apply a displacement load on one side, can we still achieve periodic boundary conditions?
Hello, according to this type of Periodic Boundary Condition implementation, it is certainly important to specify in internal nodes the applicable linear constraint equation as I showed in this video. This is what makes for a periodic corresponding edges deformation. The corner nodes are not prescribed with this equation hence they are free to be used as anchor points to apply and impose the applicable/desired loading type. If you do what you suggested in the second part of your question, you will see a deformation but only the corner nodes will before and the inside nodes will not follow suit as they have not memory of what the corner nodes are doing. The linear constraints equations (imposed on internal nodes) prescribe the kinematic linking that will connect what the corner nodes are doing to the internal nodes. I hope the explanation makes sense.
Perhaps my question wasn't clear enough, my apologies. What I meant to ask is: why are the constraint equations for the nodes along the edges combined with those for the corner nodes? I believe that in finite element analysis, the transfer of displacement loads occurs through shared nodes, and there is no need for additional displacement constraints between nodes. I would like to know if there are any special considerations for the periodic boundary conditions at corner nodes? Also, are there any special aspects to the periodic boundary conditions along the edges and at the corners of a 3D Representative Volume Element (RVE)?@@MichaelOkereke
Thanks for your question! I understand the confusion and I'll do my best to clarify it for you. You are right, that it might seem strange that there is a combination of constraint equations. The reason for this is that I am using a slightly different formulation of periodic boundary condition which a few authors use. Instead of supplying a strain tensor during the simulation, you would rather supply a displacement. That displacement is applied to an un-attached corner node. If left unattached from teh generality of the model, it will deform but that deformation will not be transferred to the full model. The solution is to then use kinematic constraints to link corner nodes to inside nodes. The inside nodes have also been prescribed with kinematic constraints themselves. This way, the corner nodes become anchor points for imposing loads, and those are then linked to internal nodes which then make for transfer of loads from an initially detached corner nodes to a later kinematically-linked corner nodes with the inside nodes. You might be confused but I am trying my best to explain. Look at the equations I used in the video again and see if you understand. I explained this more in my book which you can see here: link.springer.com/chapter/10.1007/978-3-319-67125-3_8 which is Chapter 8 where I discussed these ideas in more detail.
Thanks very much. I seem to have some understanding, but I still need to carefully study the book you wrote. I would also like to ask: In your video, are the elastic parameters predicted the same when displacements are applied at the corner points and when displacements are applied across all boundary nodes?@@MichaelOkereke
Thank you for the video! I just wondering is it possible to apply PBC in a macro-scale model while we're intersting in discretizing full-scale model into smaller finite periodic model? Also, I found quite a few resource in YT showing PBC application with the thermal analysis. Appreciate if you could emphasize on that!
![[LIVE] : ONE ลุมพินี 91 | คู่เอก "คมอาวุธ vs อเล็กเซย์"](http://i.ytimg.com/vi/V0RkEfYFsgM/mqdefault.jpg)
I have two questions, that I am still confused on. Hopefully you can answer. 17:38
First, why did you not connect node 3 to anything? Why was N4 and N1 used instead of N3 and N2.
Second, Lets assume you are applying a uniform displacement in the Z-direction that starts at NC and goes to ND. what corner/retained nodes would I use to connect my internal nodes?
Hello @Chase, thanks for the comment. I will attempt to answer.
1. Node 3 is called a slave node because, as a consequence of how the kinematic equations are defined, the node 3 adopts the degrees of freedom of nodes 2 and nodes 4 depending on the loading type. So, it has to be a slave node, and hence is not included.
2. The deformation along the Z-direction is slightly different. I wrote about this in the paper: doi.org/10.1016/j.commatsci.2012.12.036. If you read through it, you will see how I dealt with loading in the Z-axis, just a light change to the formulation already discussed in this video but certainly do-able.
Hello , Dr.Michael. Is there a description of PBC loading for the 3D RVE model in this paper which you mentioned above
Honestly the best channel in this regards which I have ever seen. Thanks a bunch Dr.
Thanks too.
Your videos are very good. Thank you. I appreciate the way you have to present and explain the topics. Definitively your videos are between the bests in abaqus explanation. Please continue creating more videos.
Thanks very much for the kind comments. I will keep going.
Thank you Dr. Okereke for a detailed explanation about PBC. I would be waiting for your video on application of PBC on non-periodic meshes.
Hello @Nishant Mistry, thanks for your interest in the channel. Of course, I will be looking into PBCs for non-periodic meshes, in future.
This video is very helpful. Eagerly Waiting for next two videos . Thanks for uploading this . This is the only video of PBC on TH-cam to describe it in such a nice manner.
You are most welcome
@@MichaelOkereke sir I have doubt, what about the N3 node. Any special treatment for that .?
Thank you DR. Okereke for the video of PBC, I hope you can publish some videos about the detailed PBC settings or whole simulations of woven fabric under tension
Thank you very much for your videos, Dr Okereke! They are all very helpful! It would be very interesting to learn how to apply PBCs on non-periodic meshes!
Hello @Athina, thanks for your interest in the channel. I am certainly interested in non-periodic meshes and have published about it which you can read here: doi.org/10.1016/j.compstruct.2016.10.114. I will make a series of videos about this in future. Please keep watching this space.
@@MichaelOkereke Thank you for your reply, Dr Okereke! I have read your work and I am in the process of altering my Periodic boundary conditions code by adding interpolations, as it is needed in my PhD project. Your publication has been very useful to understanding the concept! I will be checking your page for more videos!
Well done @Athina Kontopoulou, kind regards.
Thanks you Dr. Okereke for such amazing lecture. 🙏🙏🙏🙏🙏
You are very welcome @Sandeep Kr. Gautam. I am glad you found the lecture useful. Any suggestions for future videos are always welcome.
Thank you for the video. Was waiting for one like this.
Glad it was helpful!
Thank you for making this video. Great help！
Glad it was helpful!
Excellent video with high quality! I am quite interested in set a period boundary condition for non-period mesh. Could you please make one? Appreciate that!
Noted... thanks.
Hi Dr. Michael. Thank you very much for making the concept of PBC so lucid. Could you please make a video on non-periodic mesh ?
Hello @Abu, thanks for your kind comments. I have a plan in future to make a series of videos on non-periodic meshes so watch this space.
Thank you very very very much...sir.....love from india..best wishes from my research team
Thanks Subrat. I am going to make two more videos which will show you how to apply PBCs in ABAQUS and hopefully it will help you with your questions.
@@MichaelOkereke That will be very kind of you sir
@@MichaelOkereke Sir kindly make it for a 2D as well as 3D RVE like you did for dirichlet boundary condition
great video, hope your non-periodic mesh tutorial coming soon!!
Coming soon in deed Chunxu! Keep watching and thanks for your interest in the channel.
Please make video on application of PBC on non-periodic meshes.
Noted and thanks for the comment.
Thank you for this video.
I wonder if there is a reference for mixed BCs and how to deal with them.
Hello Ahmed, it is really a good question you ask here. I have done some modelling in the past with mixed BCs and so will try and do a demonstrative video about this.
Very interesting video to understand the Periodic Boundary Condition. But I would like to understand the difference between the representative volume element (RVE) and studying a normal specimen as the simulation of lab experiments and also the difference RVE and X-symmetry or Y-symmetry sections. Thanks in advance
Hi John, thanks for your interest in the channel. Representative volume elements are virtual domains that can be used as a substitute for the normal specimen. It is expected to give results that are comparable to normal experiments. Where you are finding it difficult to undertake the simulation of the normal specimen, then an RVE will be cheaper on computational time and can still give you good results.
On your second question on RVE, X- and Y-symmetry sections, these are related. The X- and Y-symmetry is often used when identifying an RVE for a material. They are not the same but if you are looking to isolate an appropriate RVE for a physical domain, it is quite normal and common to consider the use of the X- and Y-symmetry of the material/domain to help you.
@@MichaelOkereke Thanks for your explanations but I have to use the Periodic Boundary Condition (PBC) whenever I modelling RVE or I can use the normal boundary conditions like fixed, hinge, roller too. If so, I would like to know when shall I use PBC, I mean how can I choose to use PBC or normal boundary conditions. Thanks in advance
Thank you for the video! I just wondering is is possible to apply PBC in a macro-scale model while we're intersting in discretizing full-scale model into smaller finite periodic model? Also, quite found a few resource in YT showing PBC application with the thermal analysis. Appreciate if you could emphasize on that!
Yes you can! I will think about the thermal analysis aspect.
Hi, Dr, Michael. Thanks very much for your video. I am recently researching helical structures, which also use PBC. However, that is more complicated because the canonical equation used inside is nonlinear and sometimes has a displacement coefficient. Therefore, I have to use the user-defined MPC inside ABAQUS, which I think is not so easy to implement and I still have some confusion about this subroutine. Could you please take a video and share with us some experience?
Hello Pan, thanks for the query. It does sound you are dealing with a really challenging task. If you can, share a paper about your problem and I can see if I'd better understand it.
I have not used MPCs for applying PBCs but like you said it all depends on the canonical equations.
I discussed this extensively in my FE book. If you have it look at the section about canonical equations and boundary conditions, it might help.
I do need further information before I can consider it for a future video request. Cheers.
Hello Dr Okereke, I really learnt a lot on this video. I am definitely subscribing to the channel. I am not an ABAQUS user, I have been using COMSOL for modelling and simulation so I couldn't implement the ideas in the video. Regardless of this, I learnt a lot from the explanation. Do you use COMSOL? If yes, can you do a lecture on using Periodic flow conditions in Fluid Mechanics using COMSOL? Thank you.
Hello @Oluwaseyi Ayeni, thanks for the comment and am glad you found the videos helpful. I do not have much experience with COMSOl and so unable to help with Periodic Flow Conditions in Fluid Mechanics. Good luck with the research.
Great learning insights, thank you for simplified explanation
You are welcome Mayank! I strive to communicate things in a way that my students understand better. Thanks for your interest in the channel.
Hi, this is very interesting and well explained video. i have some question outside from this topic. how to analyze nonlinear geometrical behaviour of a 3d truss under externally excited harmonic force. how to determine their displacement and velocity w.r.t time for time domain and frequency domain analysis.
another question how to select initial condition for dynamic problem. pls response my query.
I do not work with 3D truss structure so unable to answer this query.
Great video! Would the same concepts presented apply to FEM for Electromagnetics (i.e. Electric field)? Also, is there any special consideration for when there are multiple materials?
Hello @Jake, I believe this will apply also even for our electromagnetics field, depending on what type of field you are using. The method shown here works on Dirichlet-type boundary conditions, in which case, you specify define (constant) values at nodes at a given time-step during the simulation. In our case, if you can specify definite electric field to nodes in the boundary, then this method should work. However, it your electric field is a Neumann type boundary condition (in which case, it is not a predefined value but a traction, concentration, flux term), then this will not work. You really need to give it a go by modelling your problem and running the software on it to see if it generates a PBC-enabled RVE which you subsequently run to see what the results will be like. Good luck!
Dear Dr. Michael, just noticed that the corner node N3 isn't tied to anything, just having trouble understanding how is this gonna work?
Hello Haowei, I get the question. The N3 is a slave node, it inherits the degree of freedom of N1 based on the prescribed canonical equations.
For the corner Nodes, you missed N3? Is it deliberate?
Hello @Johnson, I did not miss N3 deliberately. It is a slave node and inherits the deformation of other nodes, through the specified kinematic equation. I had provided further explanations in other comments on this video, so look at other comments and see my explanation.
EasyPBc was not created by just
a youtuber. He's a distinguished academic, Sir. Nice video!
Hello @Johnson, you are right, the developer (Dr Sadik Omirey) of EasyPBC is definitely an academic. While making this video, the reference to TH-camr was what came first into my mind but I do acknowledge that Dr Omairey is an academic as well as a TH-camr, just like myself.
When picking retained nodes that will be coupled with the internal nodes, those retained nodes have to be the ones that are influencing deformation on the entire system?
Hello @Chase, the retained nodes are essentially the nodes at the corners N1, N2, N3 and N4. However, N3 is a slave node, so unnecessary. YOu may like to look at this video where I explained more about applying, uniaxial, shear and combined loading using the retained nodes: th-cam.com/video/CqxdL0X8qec/w-d-xo.html . Let me know if you have any more questions.
Hello, Dr.Michael. I have another question. What if I want to give both uniaxial deformation and shear deformation on a RVE model , can I make it possible? I mean , how can I deal with this situation? I am really confused.
I have no idea about how to fix the retained nodes in this situation.
Follow the approach I used in the video
Here is a video I made on this issue:
th-cam.com/video/CqxdL0X8qec/w-d-xo.html
Very helpful tutorial video. Thanks for your sharing. I read your book and wonder if you can do the video on how to apply periodic boundary conditions to non-periodic mesh as you mentioned in your book and paper. Can I contact you?
Dear K M, thanks for your interest in the channel. I have the suggestion as part of my plan for the future. Keep watching. If you want to get in touch with me, you can join my CM Videos Insider Group using this link: cmvideos.ck.page/16a99bd0e3. You will check your mail to confirm subscription and then you can reach out to me as a CM Videos Insider.
Hi, why i always must impose an strain? Are other alternative? Like solve the micromechanical problem with iterative calculation
Hello, thanks for the query. I am using a particular method in generating the PBC response which requires specifying a Dirichlet BC e.g. displacement at a retained/corner nodes. Since the RVE has kinematical constraints enforced using the *EQUATION command in ABAQUS, any movement at a corner nodes will cascade down the material (periodically) leading to the expected behaviour.
I know some other authors use strain tensor (which they introduce into the model), but this is not how I do it. It is also a valid approach. I am not sure what you mean by solving the micromechanical problem with an iterative calculations, sorry!
@@MichaelOkereke hi, thanks for the answer.. my question go on the direction of plastic deformation but is not the case. About your answer, i have a question.. why PBC requires dirichled bc?
@@MichaelOkereke Hi, thanks for the answer.. my question are about non-linear and path dependent, but is not the case.. but i have another question.. why did you use Dirichlet BC?? where can i find literature about that and.. what is the model with strain tensor?? thanks
PBCs in the way I use require that you specify a displacement at a node hence the Dirichlet approach. It is only the displacement at one node that is Dirichlet. The other nodes are imposed with PBCs.
There are so much literature on PBCs but this was one that was particularly helpful when I was learning about this:
1. Kuznetsova paper: link.springer.com/article/10.1007/s004660000212
and
2. My paper: doi.org/10.1016/j.commatsci.2012.12.036
Hopefully these will help you.
U10y and U4y are going the opposite direction, they're supposed to go the same direction right?
Definitely @Tonda, the directions at 8:07 are wrong. Well spotted. Same applies to U5y and U9y. They should be pointing in same direction. Thanks.
@@MichaelOkereke Thank you! Do you mean U10y and U4y are pointing in the negative Y direction together? Also, U5y and U9y are pointing in the negative Y direction together?
Sir I need your help regarding something related to my project in randomly oriented fiber reinforced composites. Where can contact you?
Hello Chirag, thanks for your interest in the channel. If you want to contact me directly to discuss your project challenges, then please send an email directly to: michael.okereke@cmvideos.org.
It is a bit more complicated. When N2 moves by delta_x and N1 is constrained (fixed) then UN2=UN1 cannot be true. Actually UN2-UN1=delta_x not zero. Similarly UNB-UNA=delta_x etc. I guess this method does not allow to prescribe effective stress load on the edges, or does it?
Hello Robert, thanks for your comment. It is indeed complicated, the whole PBC stuff. I wanted to make some clarifications to your comments.
First, N1, N2, N3 and N4 are called constrained nodes, so they are not prescribed with periodic boundary conditions. I use them to apply a required loading type to the model. So, when you say if UN1 is fixed say in the x-direction, that means the displacement there is zero. However, when UN2 is imposed with a delta_x load, then UN2 will have a dispalcement of UN2 = delta_x. As a consequence too, UN2 - UN1 = delta_x, as you rightly posited. However, at the onset of the model, without delta_x imposed on the system, UN1 = UN2 or in other words, UN1 - UN2 = 0, but when there is an imposed load, then the zero is replaced with delta_x. I believe you got this correctly.
However, your second comment on UNB - UNA = delta_x is not necessarily true. This is because those are internal nodes that will not automatically take the value of delta_x. The only way they will take that value is when you kinematically link N1-N2 to NA-NB which is the equation I described as: UN1 - UN2 = UNA - UNB. If the system is homogeneous without any microstructural heterogeneity, then automatically, UN1 - UN2 = delta_x and then your comment is correct. However, as we are looking at heterogeneous systems, it is better to use the UNA - UNB nodal values as you travel along the edges (considering the internal nodes). In some instances, those nodal values may even result into negative values depending on the environment of the microstructural constituent of the RVE. I believe we are saying the same things but your comment relates for a special case where the domain is heterogeneous in which case the edge will deform uniformly (as if you imposed a dirichlet boundary condition to it).
On the last comment around prescribing effective stress load on the edges, I am not sure I understand that. I know there is another PBC method where you do not explicitly impose delta_x to the edges. The other method is the strain tensor method, where you will apply a strain field to the domain using a virtual node, which is kinematically linked to a part of the model. The method uses the strain field to multiply the set of edge dimensions, which will again result into a set of displacements [delta_x delta_y delta_xy] and the like. In this case, the user will focus on the expected strain in the model as an input. The stress will result after the FEA simulation. I do not know of a case where effective stress is imposed as an input to the model. Please point me to any literature that deals with PBC in FEA like that.
Thanks for your comments and I appreciate you thoughts.
Is it necessary to constrain the nodes on the edges and corners? If we only constrain the corresponding nodes on the edges and then apply a displacement load on one side, can we still achieve periodic boundary conditions?
Hello, according to this type of Periodic Boundary Condition implementation, it is certainly important to specify in internal nodes the applicable linear constraint equation as I showed in this video. This is what makes for a periodic corresponding edges deformation. The corner nodes are not prescribed with this equation hence they are free to be used as anchor points to apply and impose the applicable/desired loading type.
If you do what you suggested in the second part of your question, you will see a deformation but only the corner nodes will before and the inside nodes will not follow suit as they have not memory of what the corner nodes are doing. The linear constraints equations (imposed on internal nodes) prescribe the kinematic linking that will connect what the corner nodes are doing to the internal nodes. I hope the explanation makes sense.
Perhaps my question wasn't clear enough, my apologies. What I meant to ask is: why are the constraint equations for the nodes along the edges combined with those for the corner nodes? I believe that in finite element analysis, the transfer of displacement loads occurs through shared nodes, and there is no need for additional displacement constraints between nodes. I would like to know if there are any special considerations for the periodic boundary conditions at corner nodes? Also, are there any special aspects to the periodic boundary conditions along the edges and at the corners of a 3D Representative Volume Element (RVE)?@@MichaelOkereke
Thanks for your question! I understand the confusion and I'll do my best to clarify it for you.
You are right, that it might seem strange that there is a combination of constraint equations. The reason for this is that I am using a slightly different formulation of periodic boundary condition which a few authors use. Instead of supplying a strain tensor during the simulation, you would rather supply a displacement. That displacement is applied to an un-attached corner node. If left unattached from teh generality of the model, it will deform but that deformation will not be transferred to the full model.
The solution is to then use kinematic constraints to link corner nodes to inside nodes. The inside nodes have also been prescribed with kinematic constraints themselves. This way, the corner nodes become anchor points for imposing loads, and those are then linked to internal nodes which then make for transfer of loads from an initially detached corner nodes to a later kinematically-linked corner nodes with the inside nodes.
You might be confused but I am trying my best to explain. Look at the equations I used in the video again and see if you understand.
I explained this more in my book which you can see here: link.springer.com/chapter/10.1007/978-3-319-67125-3_8 which is Chapter 8 where I discussed these ideas in more detail.
Thanks very much. I seem to have some understanding, but I still need to carefully study the book you wrote. I would also like to ask: In your video, are the elastic parameters predicted the same when displacements are applied at the corner points and when displacements are applied across all boundary nodes?@@MichaelOkereke
So when are you going to explain how deal with non priodic mean...
Good point @Hossein, I have the ambition to do so but other stuff keep getting in the way. Hopefully one day I would.
@@MichaelOkereke I am eagerly waiting...
Thank you for the video! I just wondering is it possible to apply PBC in a macro-scale model while we're intersting in discretizing full-scale model into smaller finite periodic model? Also, I found quite a few resource in YT showing PBC application with the thermal analysis. Appreciate if you could emphasize on that!
Yes you can! I will think about the thermal analysis aspect.