POWER SCALING LAWS AND DIMENSIONAL TRANSITIONS IN SOLID MECHANICS

Physicists have often observed a scaling behaviour of the main physica l quantities during experiments on systems exhibiting a phase transiti on. The main assumption of a scaling theory is that these characterist ic quantities are self-similar functions of the independent variables of the phenomenon and, therefore, such a scaling can be interpreted be means of power-laws. Since a characteristic feature of phase transiti ons is a catastrophic change of the macroscopic parameters of the syst em undergoing a continuous variation in the system state variables, th e phenomenon of fracture of disordered materials can be set into the w ide framework of critical phenomena. In this paper new mechanical prop erties are defined, with non integer physical dimensions depending on the scaling exponents of the phenomenon (i.e. the fractal dimension of the damaged microstructure, or the exponent of a power-constitutive r elation), which turn out to be scale-invariant material constants. Thi s represents the so-called renormalization procedure, already proposed in the statistical physics of random process. Copyright (C) 1996 Else vier Science Ltd.