Is it possible to calculate the bending rigidity of a nanomaterial by applying a force vertically at its mid-point using SMD (constant velocity) by keeping the two ends fixed? By this, we can measure the vertical deflection. However, how can I compute the bending rigidity from this vertical deflection? Thank you.

Please post questions about LAMMPS in one of the LAMMPS categories, *not* in the unrelated Materials Project category.

Actually, your question is not even so much about using LAMMPS but about some science problem.

If you want to figure out what you need to compute you first need to figure out how it is defined/derived and what kind of data you need to compute. You will not likely find this in the LAMMPS documentation of from asking other LAMMPS users, but more likely in the published literature where people have computed such property from MD simulations. From the outside, however, it looks quite a lot like you are trying to apply macroscopic physics to the nanoscale which is very likely to fail. But you really need to hit the literature to know for certain.