Mechanical percolation is a phenomenon in materials processing wherein ‘filler’ rod-like particles are incorporated into polymeric materials to enhance the composite’s mechanical properties. Experiments have well-characterized a nonlinear phase transition from floppy to rigid behavior at a threshold filler concentration, but the underlying mechanism is not well understood. We develop and utilize an iterative graph compression algorithm to demonstrate that this experimental phenomenon coincides with the formation of a spatially extending set of mutually rigid rods (‘rigidity percolation’). First, we verify the efficacy of this method in two-dimensional fiber systems (intersecting line segments), then moving to the more interesting and mechanically representative problem of three-dimensional fiber systems (cylinders). We show that, when the fibers are uniformly distributed both spatially and orientationally, the onset of rigidity percolation appears to co-occur with a mean field prediction that is applicable across a wide range of aspect ratios.
