Author(s)

A. Carpinteri & P. Cornetti

Abstract

Scaling laws in solid mechanics: static, kinematic and energy dissipation aspects A. Carpinteri, P. Cornetti Department of Structural Engineering and Geotechnics, Politecnico di Torino, Italy Abstract Several experiments have pointed out the size effects affecting the quasi-brittle material parameters. In the present paper it will be shown how the related scaling laws can be considered as a consequence of porosity and microcrack distributions with self-similar patterns. Renormalization procedures applied to the damage process lead to the definition of anomalous fractal quantities, whose values govern the rupture phenomenon independently of the structural size. Our analysis allows a global explanation of the size effects affecting the cohesive law and yields to a fractal cohesive law which is a true material property. Then, a universal relationship among the exponents of the scaling laws for strength, critical displacement and fracture energy, is found. The fractal model is

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