Saturation effects in ac + dc driven Frenkel–Kontorova model

•We examine behavior of different commensurate structures in the ac + dc driven FK model.•Dissipative overdamped dynamics of series of coupled harmonics oscillators subjected to ASDP is considered.•Reduction of degrees of freedom in highly deformed systems is detected.

Properties of the Shapiro steps in different commensurate structures of the ac + dc driven Frenkel–Kontorova model with asymmetric deformable substrate potential have been examined. Deviation from the sinusoidal potential produces appearance of large subharmonic steps. In general, different commensurate structures respond differently to the applied force and have different velocities. The results have shown that after shape parameter gets some critical value, there is no difference in the behavior of Shapiro steps for different commensurate structures. The step size and the critical depinning force for different commensurate structures saturate to the same values, due to reduction of degrees of freedom with the large deformation of potential.