Can we create a thin 3D model by reducing the model thickness in the z-axis, for example, in LAMMPS and consider it infinite by applying the periodic boundary condition? I am confusing about the periodic boundary condition for solid materials.

Check the literature on slab models. A slab is a model of a surface where you have two surfaces exposed along one of the three Cartesian axes in an orthorhombic box (more complicated cases are possible, e.g. monoclinic and hexagonal boxes). The important point is that there are two interfaces.

It is not necessary to have a non-periodic boundary on the direction perpendicular to the surface: that could be the case for a surface embedded in a solvent. In this case, you may want to make the perpendicular direction large enough to minimise the interactions between the periodic replicas of the slab.

This is an example of a polymer membrane (in the center) encased in water:

Yes, it is an infinite system, but it is still subject to finite size effects. Due to the periodicity the length of the box dimension limits which frequencies can be represented. The shorter the box dimension, the higher the minimum frequency is and that can have significant impact on determining properties of the sample. Often low frequency fluctuations are required to trigger activated processes (e.g. phase transitions) and then a too short box dimension can significantly suppress those fluctuations.

I think applying periodic boundary conditions in one axis in solids does not make them infinite in that axis (does not apply the plain strain condition).

I am modeling a cantilever elongated in the X and Z planes with a thickness of “t” in the Y axis. The thickness of “t” is much smaller than “b”. The PBC is applied in the Y axis to (1) reduce computation time and (2) simulate an infinite thickness. A load was applied on the tip and then removed, and bending was observed. However, the modeled cantilever does not appear rigid and behaves more like a string or rope.

I think this is because of the small cross-section in the ZY plane. The cross-sectional dimensions should be sufficient to provide rigidity to the cantilever. Therefore, I believe the applied periodic boundary condition in this model does not accurately simulate a thick or infinite dimension in the Y axis.

If you have a periodic boundary in one direction and the atoms fill the box in that direction, you have no surfaces and thus a bulk system that is replicated an infinite number of times in that direction like a unit cell in a crystal. That is just how periodic boundaries work and that is a fact not a “thought”.

It is impossible to comment on this because there is no way to reproduce what you are saying as well and no way to confirm that your input is actually representing what you say it does.

The statement

raises some red flags. Choices in a simulation should never be motivated by what takes less simulation time first but always by what is necessary to correctly represent the system you want to model. Consideration of what is computationally more efficient are a secondary concern and should never impact the validity of the model.

That suggests that your simulation input is not correct, either geometry, or settings, or potentials or a combination. Impossible to say from the outside which.