If I understand correctly, you want to know which plies are above and below your delamination given that the latter is at 0.1 of the thickness and that the laminate is [45/0/-45/0/45/0/-45/0/45/0]2s.

Assuming that the numbering starts from the upper ply and since your laminate is 40 plies thick, your flaw would be between plies 4 and 5. That is:

[[45/0/-45/0] flaw [45/0/-45/0/45/0] [45/0/-45/0/45/0/-45/0/45/0] [-45/0/45/0/-45/0/45/0/-45/0]2]

However, looking at the images you provided, you intend to use a symmetry condition in your FEM modelk. Then, be aware that if one is to use symmetry conditions in FEM, it implies BOTH geometric symmetry AND material symmetry. In the case of continuous fibre composites of unidirectional plies stacking, the material symmetry condition is not met. That is, for a given position through the thickness, using a symmetry condition will make the fibre orientation symmetric, resulting for example in 45 and -45 fibre orientations for the same ply along the laminate length and/or width (see attached sketch). That is most likely not what you are trying to model .

The take away is that symmetry conditions for FEM of composite materials are to be used carefully, if at all.

Best regards,

Laurent

thank u very much sir for such a comprehensive answer i m really thankful for that ...

kindly can u tell me if i m going to use a quarter model for my simulation so as it can be seen that there is no symmetry in the thickness direction so do i have to use the total stacking sequence(40 plies) in the quarter model...just like u provided or it will be different ,,?kindly i would be glade if u could just send me the stacking sequence i m going to use in the QUARTER MODEL for simulation ,,,here i m also attaching a paper there is no explanation about the stacking sequence that why i m stuck here..

thank u

best regards

ismail

Based on what I know from your problem, your damaged laminate does not have any symmetry conditions that can be exploited in FEM. Through the thickness, the presence of the delaminated zone breaks the symmetry and through the length and width, symmetry conditions would change the orientation of fibers along those directions on each side of the symmetry plane.

For as far as I can tell, using symmetry conditions on the length and width of a composite plate modelled in FEM is only suitable when the in-plane global behaviour of an homogeinized shell is used. By homogeneized, I mean a orthotropic single layer element with equivalent in-plane properties to that of the layered plate. Moreover, that is only really good for symmetric and balanced laminates (ie without material couplings).

In your case, and in the case of the paper you linked to, the ply level behaviour is to be analyzed and thence, no symmetry conditions will provide adequate representation of a real laminate. To me, despite coming from well known authors, the paper you link to fails to provide an adequate modelling of a true laminate behaviour because it uses unsuitable symmetry conditions along the length and width.

In my opinion, you have no choice but to model a full plate and its whole layer stack.

  Sir Laurent Cormier 

Thank u very much for such quick response

Actually after studying ur answers i just modeled the full plate with the same stacking sequence in upper and lower parts as U PROVIDED above   ,,,,and seems to be working fine,delamination growth and its initiation is same as in the paper   BUT

as i m just validating this paper to validate my modeling technique for delamination buckling my reaction forces are not matching with the paper 

i m regenrating the graph in FIGURE-5 OF THE PAPER

Actually my forces are in Kilo Newtons   while in the graph applied max force is 5842N

I dont know what seem to be the problem because out of plane displacement  of point U and L  (AS IN THE FIGURE-1)for full model  are also same but forces are in KN ..I M USING ABAQUS 6.14 ....

i can send u my cae file if u want to take a look  please give me some suggestion regarding this .

thank u very much for ur valuable time 

best regards

I'm sorry but I won't be able to look at your files. However, if you modelled the full plate, your results should differ somewhat from those of Wang et al as you are not modelling the same conditions as he does. The symmetry condition should affect the results as discussed before. Admittedly, the difference might not be huge, but it should exist. I realize just now for example that if the laminates above and under the delamination do not exhibit strong couplings, results should be quite close with or without the symmetry conditions.

As for the units, in FEM the user is responsible for making sure that all inputs are in consistent units. Then, for for forces in N, and length in m, stress would be Pa and work in Joules, etc. Your error probably only result from inconsistency in input units.

thank u sir ...

 let me model it in meters and then compare my result accordingly    as was modeling it in mm  length and width  and delamination size and then converting accordingly the materials properties in to mm ,[Pa into N/mm2] ,,,that might be the reason  OF IT,,,,I Will let u know

thank u for ur time

best regards

ismail