Planar random networks with flexible fibers

The transition in random fiber networks from two-dimensional to asymptotically three-dimensional planar structure with increasing coverage ¯c (mean fiber length per unit area) is studied with a deposition model. Network geometry depends on the scale-free product of fiber length and ¯c at low ¯c, and on another scale-free product of flexibility and the width-to-thickness ratio of fibers at high ¯c. The structure becomes three-dimensional or decouples from the substrate faster when fibers are stiffer. Roughness of the free surface decreases with increasing fiber flexibility.