Fractal fragmentation theory for shape effects of quasi-brittle materials in compression

Size effects on dissipated energy density and strength for quasi-brittle materials in compression are analysed theoretically and experimentally herein. By using a fractal fragmentation approach the dissipated energy density of a structural element under compression is deduced. In addition, the dissipated energy density and the strength for geometrically similar structural elements under compression, by varying their size, are obtained. Finally, a comparison between theoretical predictions and experimental results is presented for plane as well as fibre-reinforced concrete. The size effects on dissipated energy density and compressive strength are captured by the proposed model in a satisfactory way.

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