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The hypothesis of a damage band characterized by microcrack distributions with fractal patterns leads to the definition of a new quantity, the fractal strain, whose value governs the rupture independently of the structural size. The fractal nature of the damage process is able to explain the rising tail of the cohesive law observed while increasing the size, i.e. it clarifies the scaling law of the critical displacement. Together with the fractal stress introduced by the first author, it is possible to define a fractal cohesive law which is scale-independent, i.e. a material property. The fractal model is applied eventually to some experimental data.