Comparing multi-scale cracking mechanisms in man-made composites and natural materials

Man-made composites, like reinforced and fiber-reinforced concrete elements, behave similarly to natural composite structures (e.g., brittle rocks lying on a ductile substratum). In both cases, the cracking phenomenon of brittle layers depends on the scale of observation and is ruled by the Golden Ratio. Thus, a unique size-effect relationship, herein called Golden Scaling Law (GSL), is introduced and used to predict the crack pattern of concrete and rock structures. In accordance with several experimental data, GSL permits to calculate the values of crack width and crack spacing when the geometry of crack patter is known at a lower scale. Moreover, GSL can be applied to large composite structures without knowing the material performances, but by testing prototypes of lower dimensions.