  In this paper, a computational model in (2+1)-dimensions which simulates the
rupture process of a fibrous material submitted to a constant force $F$, is
analyzed. The roughness exponent $\zeta$ at the boundary that separates two
failure regimes, catastrophic and slowly shredding, is evaluated. In the
catastrophic (dynamic) regime the initial strain creates a crack which
percolates rapidly through the material. In the slowly shredding (quasi-static)
regime several cracks of small size appear in all parts of the material, the
rupture process is slow and any single crack percolates the sample. At the
boundary between these two regimes, we obtained a value $\zeta\simeq 0.42\pm
0.02$ for the roughness exponent, in agreement with results provided by other
simulations in three dimension. Also, at this boundary we observed a power law
behavior on the number of cracks versus its size.

Statistical Mechanics