Self-affine nature of the stress-strain behavior of an elastic fractal network

The stress-strain behavior of fractal networks possesses self-affine scaling associated with statistical scale invariance of damage patterns. We found that the damage part of stress-strain curve of fractal network and the corresponding rupture line are characterized by the same scaling (Hurst) exponent, H, which is not universal, rather it depends on the network fractal dimension as H= D_B-1. Furthermore, the same exponent governs the changes in the stress-strain behavior as the strain rate increases. These results were reproduced by Monte Carlo simulations using a fractal version of fiber bundle model.