Fractals to Model Hierarchical Biomaterials [chapter]

Alberto Carpinteri, Pietro Cornetti, Nicola Pugno, Alberto Sapora
2008 Advances in Science and Technology  
Many biological materials exhibit a hierarchical structure over more than one length scale. Understanding how hierarchy affects their mechanical properties emerges as a primary concern, since it can guide the synthesis of new materials to be tailored for specific applications. In this paper the strength and stiffness of hierarchical materials are investigated by means of a fractal approach. A new model is proposed, based both on geometric and material considerations and involving simple
more » ... e formulas. Strength of hierarchical materials Let us consider a tensile test on N-hierarchical fibre-reinforced bar. Its cross-section is composed by hard inclusions embedded in a soft matrix and it is represented in Fig. 1 . The nominal stress σ 0 could be evaluated by means of a recursive scheme of rules of mixture as [11]:
doi:10.4028/3-908158-15-x.54 fatcat:4b2boqc4czdnpkviulfnjhb65e