  The pinning of vortex lines by an array of nanoparticles embedded inside
superconductors has become the most efficient practical way to achieve high
critical currents. In this situation pinning occurs via trapping of the
vortex-line segments and the critical current is determined by the typical
length of the trapped segments. To verify analytical estimates and develop a
quantitative description of strong pinning, we numerically simulated isolated
vortex lines driven through an array of nanoparticles. We found that the
critical force grows roughly as the square root of the pin density and it is
strongly suppressed by thermal noise. The configurations of pinned lines are
strongly anisotropic, displacements in the drive directions are much larger
than in the transverse direction. Moreover, we found that the roughening index
for the longitudinal displacements exceeds one. This indicates that the local
stresses in the critical region increase with the total line length and the
elastic description breaks down in the thermodynamic limit. Thermal noise
reduces the anisotropy of displacements in the critical regions and straightens
the lines.
