Self-affine nature of the stress-strain behavior of thin fiber networks

The stress-strain behavior of toilet paper is studied. We find that the damaged parts of stress-strain curves possess a self-affine scaling invariance. Moreover, we find that the stress-strain behavior and the rupture line roughness are characterized by the same scaling (Hurst) exponent H, which is not universal: rather it changes from sample to sample. The variations on H are mainly due to fluctuations in the paper structure, which are larger than statistical errors within a sample. Furthermore, the same exponent governs the changes in the stress-strain curve as the strain rate increases. The fractal damage model is employed to explain experimental observations.