Superconductors can support large dissipation-free electrical currents only if vortex lines are effectively immobilized by material defects. Macroscopic critical currents depend on elemental interactions of vortices with individual pinning centers. Pinning mechanisms are nontrivial for large-size defects such as self-assembled nanoparticles. We investigate the problem of a vortex system interacting with an isolated defect using time-dependent Ginzburg-Landau simulations. In particular, we study the instability-limited depinning process and extract the dependence of the pin-breaking force on inclusion size and anisotropy for an emph{isolated vortex line}. In the case of a emph{vortex lattice} interacting with a large isolated defect, we find a series of first-order phase transitions at well-defined magnetic fields, when the number of vortex lines occupying the inclusion changes. The pin-breaking force has sharp local minima at those fields. As a consequence, in the case of isolated identical large-size defects, the field dependence of the critical current is composed of a series of peaks located in between the occupation-number transition points.
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