  The fragmentation of small, brittle, flexible, inextensible fibers is
investigated in a fully-developed, homogeneous, isotropic turbulent flow. Such
small fibers spend most of their time fully stretched and their dynamics
follows that of stiff rods. They can then break through tensile failure, i.e.
when the tension is higher than a given threshold. Fibers bend when
experiencing a strong compression. During these rare and intermittent buckling
events, they can break under flexural failure, i.e. when the curvature exceeds
a threshold. Fine-scale massive simulations of both the fluid flow and the
fiber dynamics are performed to provide statistics on these two fragmentation
processes. This gives ingredients for the development of accurate macroscopic
models, namely the fragmentation rate and daughter-size distributions, which
can be used to predict the time evolution of the fiber size distribution.
Evidence is provided for the generic nature of turbulent fragmentation and of
the resulting population dynamics. It is indeed shown that the statistics of
breakup is fully determined by the probability distribution of Lagrangian fluid
velocity gradients. This approach singles out that the only relevant
dimensionless parameter is a local flexibility which balances flow stretching
to the fiber elastic forces.
