Mineralized bio-composites, such as the tooth enamel and the prismatic and nacreous layers of sea shells, are typically composed of a hard mineral phase in the forms of bricks, prisms or rods that confine thin interfaces made of a soft proteinaceous matrix material. Measuring the nano-mechanical properties of such bio-composites by nano-indentation is an extremely challenging task due to the emergence of interactions between the stress fields at the different phases - which affect both the indentation profile and local stiffness of the material. In this study we employ Finite-Element simulations to quantify the effect of the indentation depth and the difference in mechanical properties of the individual bio-composite phases on the resultant nano-mechanical properties of the bio-composite material. Two distinguished indentation modes were identified: (1) soft-phase dominant mode that arises in shallow indents or wide interfaces and (2) hard-phase dominant mode that arises for deep indents of thin interfaces. By employing a non-dimensional analysis and a series of FE simulations it is found that the soft-phase mode the nano-mechanical properties are found to be determined merely by the indentation depth and the properties of the soft phase - regardless the hard phase characteristics (and vice versa for the hard-phase mode). Closed-form analytical formulae that characterize these relations were established and verified for a wide range of possible bio-composite indentation configurations.
Based on these analytical findings we developed a novel testing protocol for nano-indentation of bio-composites materials - by which the mechanical properties of the individual phases can be back-calculated by using only two nano-indentation testing measurements, one at each of the above modes. This methodology can potentially be employed for the analysis of various types of nano-composites, both biological and synthetic, and to shade a new light on the fundamental mechanical properties of their individual phases - directly within the composite complex.