We numerically investigated the transport, deformation and buckling events of an isolated elastic fiber in Taylor-Green vortices and studied the dynamics of long filaments in homogeneous isotropic turbulence. The fiber is modelled by an assembly of spherical beads. The contact between beads enforces the inextensibility of the filament while bending is accounted for by the Gears Bead Model (GBM) proposed by Delmotte et al. (2015). In the cellular Taylor-Green flow, the buckling probability is a function of a dimensionless number, called Sperm number, which is a balance between the compression rate of the flow and the elastic response of the filament. The shapes of the filament and its ability to buckle have been successfully validated through comparisons with experiments from the work by Quennouz et al. (2015). The deformation statistics of long flexible fibers in sustained homogeneous isotropic turbulence were analyzed for various flow and fiber material conditions. Two regimes have been identified depending on the ratio of fiber length to persistence length which is a measure of turbulent forcing to flexibility. The numerical results are in good agreement with existing experimental data (C. Brouzet et al., Phys. Rev. Lett. 112, 074501 (2014)) validating the assumptions of our model for the configurations we investigated.