Analogies in fracture mechanics of concrete, rock and ice

Both in architecture and arts, the golden ratio has been taken into consideration most exclusively for its geometrical properties. Specifically, among all the proportions, the golden ratio can inspire beauty and aesthetic pleasure. Indeed, it has driven, in an implicit or explicit manner, the construction of buildings for centuries. Nevertheless, as discussed in the present paper, also fracture mechanisms in brittle and quasi-brittle materials call the golden ratio into play. This is the case of fracture energy and fracture toughness, in which the irrational number 1.61803 recurs when the geometrical dimensions vary. This aspect is confirmed by the results of different experimental campaigns performed on concrete and rock beams and ice sheets. In other words, it can be argued that the centrality of the golden ratio for quasi-brittle structures has profound physical meanings, as it can bring together the aesthetic of nature and architecture, and the equilibrium of stress flow in solid bodies.