Thank you so much for your reply and your suggestions. Effectively, by changing the beams to links, the solver was able to go further and helped to reduce the force imbalance, and, as you mentioned, the real behavior of the fibers is orthotropic.
At the moment I am struggling a little trying to perform the "sweep mesh", since the body does not want to become "sweepable", but I will deal with it. The "Newton-Raphson residuals" is providing more information about the force convergence, and I am attacking the contact regions to see if that improves the force convergence.
Once I am able to go further than this, I will let you know.
Again thank you for your help,