Figure 7.

Principle of mechanics model owing to Gao and co-workers and application to experimental data. Gao developed a hierarchical mechanics model based on suggestions from Jäger and Fratzl, which consists of (a) a two-dimensional self-similar structure made of hard particles (black) embedded within a soft protein phase (bright grey). The composite structure at level n forms the hard particles at level (n + 1). The as-built structure is virtually loaded in tension and the basic assumption thereby is that the hard particles at each hierarchical level carry the tensile load that is transferred via shearing of the protein phase. By applying fracture mechanics concepts and geometrical considerations, Gao and co-workers developed formulae for hierarchical strength, elastic modulus and toughness. We show the applicability of the model to experimental results of real biological materials by predicting the strength of the second hierarchical level within enamel using experimental data from level 1—as can be seen (b), calculations and experiment fit quite well. Alternatively, it is possible to calculate (b) the HAP nano-fibre strength (2 GPa), which can hardly be determined experimentally. For (c) elastic modulus also, quite satisfying agreement of model and experimental results was found. Unfortunately, the model cannot be applied to the third level of hierarchy as decussation cantilevers owing to size limitations in fact contained several decussated rods, but not several aligned Hunter–Schreger bands (which would represent the ‘hard particles’ of the third level). (b) Orange regions, experimental data; blue regions, calculations owing to Gao. (c) Orange regions, experimental data; green regions, basic constituents; blue regions, calculations.