We report magnetoresistance measurements in Nb films having a periodic thickness modulation. The cylinder shaped thicker regions of the sample, which form a square lattice, act as repulsive centers for the superconducting vortices. For low driving currents along one of the axes of the square lattice, the resistivity ρ increases monotonously with increasing magnetic field B and the ρ–B characteristics are approximately piecewise linear. The linear ρ versus B segments change their slope at matching fields where the number of vortices is an integer or a half integer times the number of protruding cylinders in the sample. Numerical simulations allow us to associate the different segments of linear magnetoresistance to different vortex-flow regimes, some of which are dominated by the propagation of discommensurations (kinks).
