It is known that most natural materials exhibit hierarchical organization of matter and fractal geometries, which provide increased surface area for the same volume of material. Fractal geometry indeed permits the design of hierarchical patterns through self-similar subdivisions of basic shapes such as squares or triangles. This subdivision process can be repeated an infinite number of times, obtaining increasingly complex structures that exhibit fractal dimensions much greater than their topological dimensions.

Fractals have been employed in a large variety of fields, including biology, economy, bio-architecture, electrical engineering, and in a number of different technologies. Particularly interesting is the fractal modeling of fractures and sutures in engineering and biological systems, as well as the fractal description of the topological interlocking occurring in architectured materials that are obtained by joining similar or dissimilar materials through interfaces with complex geometry.

We presented a general purpose methodology for the design of reinforcing fibers and meshes of cement-matrix composite materials with fractal architecture, through suitable manipulation of the Koch curve construction. The analyzed reinforcements are aimed at inducing multiscale interlocking phenomena at the interface with the matrix material, due to their complex and multiscale geometry. We observed, indeed, that such elements can be regarded as hierarchical joints between different portions of the matrix, which feature fractal geometry at different levels.


3D views of Koch fibers for different complexities



Farina, I., Fabbrocino, F., Colangelo, F., Feo, L., & Fraternali, F. (2016). Surface roughness effects on the reinforcement of cement mortars through 3D printed metallic fibers. Composites Part B: Engineering, 99, 305-311.


Farina, I., Fabbrocino, F., Carpentieri, G., Modano, M., Amendola, A., Goodall, R., … & Fraternali, F. (2016). On the reinforcement of cement mortars through 3D printed polymeric and metallic fibers. Composites Part B: Engineering, 90, 76-85.


Farina, I., Modano, M., Zuccaro, G., Goodall, R., & Colangelo, F. (2018). Improving flexural strength and toughness of geopolymer mortars through additively manufactured metallic rebars. Composites Part B: Engineering, 145, 155-161.


Farina, I., Goodall, R., Hernández-Nava, E., di Filippo, A., Colangelo, F., & Fraternali, F. (2019). Design, microstructure and mechanical characterization of Ti6Al4V reinforcing elements for cement composites with fractal architecture. Materials & Design, 172, 107758.