Three different approaches for damage domain characterization in disordered materials: Fractal energy density, b-value statistics, renormalization group theory

Material characterization is usually based on the stress–strain constitutive laws directly derived from the load–displacement relations of uniaxial compression tests. This approach, which implies a uniform distribution of deformation along the specimen axis and an energy dissipation within a volume, does not permit to correctly describe the mechanical behavior and the damage evolution by varying the structural size and slenderness.In this paper, three different approaches are used to evaluate the physical dimension of the damage domain in disordered materials subjected to uniaxial compression. The energetic and the statistical methods are based on the acoustic emission monitoring technique, whereas the renormalization group procedure is based on the assumption of anomalous physical dimensions for the material properties. The three approaches agree very well in the determination of the damage domain fractal dimension.

► The damage pattern in disordered materials subjected to compression has fractal characteristics.
► Three different approaches are proposed to evaluate its physical dimension.
► The energetic and the statistical methods are based on the acoustic emission technique.
► The renormalization group procedure assumes noninteger physical dimension for the material properties.
► The three approaches agree very well in the determination of the damage domain fractal dimension.