Hi,

This seems to me a non-linearity causing by geometry, meaning that as the geometry of the plate changes (significantly) during loading, its structural stiffness evolves. Maybe, NLgeom option can help you. You can read more about it here:

https://www.researchgate.net/post/NLgeom_off_on_in_Abaqus

I agree with Mahoor.

Indeed it would be interesting to know if the laminate is quasi-isotropic or not. Moreover the slight difference in slope between region I and II may be an artifact due to the local penetration of the indenter (and the supporting frame)

Dear Mr D'Amore and Mehdikhani,

The material is quasi-isotropic. I tried to take into account the geometric non-linearity in Abaqus which showed an obviously different evolution compared to the use of linear elements. I agree with Mr D'Amore regarding the local penetration of the indenter (however difficult to model in Abaqus). What really drived me to ask the question is the detailed explanation of the attached reference.

I thank you for your reply and help. 

Yes, the geometrical non linearity depends on the laminate thickness/outer span ratio. 

In the figure you are reporting for explanation it seems that the laminate is quite thin.

Please, do not forget that the plate is not an ideal one and still contains flaws, like wet fibers, voids, misalined fibers and so on this may result in a lower modulus (Region I in your sample) at the start of the test. Then the effectiveness of the reinforcing fibers is sligthly increased (Region II in your sample). This last aspect is very much known when woven fibers are used.

 Dear Lassaad,

The paper you have attached has a completely different story than yours, unless you are also modeling nanoindentation on individual fibers. What I understood from your question is that you are modeling homogenized plies. Please read that paper carefully and the difference in scales!

Dear Mahoor,

I thank you for the advice I understand that the scale is not the same.