Stiffness of the extrafibrillar phase in staggered biological arrays

A number of important biological tissues such as nacre, tendon, and bone consist of staggered structural arrays as universal motifs. Such arrays usually include stiff fibril-like (or plateletlike, or needlelike) elements embedded in an extrafibrillar (XF) phase. This work discusses the effect of the stiffness of such an XF matrix on the elastic properties of the resulting staggered composite. In the case of most biological composites, this XF stiffness is hardly accessible and very little data are available. We develop an analysis based on previous analytical formulation that results in a relation between the XF modulus and the deformations of the staggered particles. This analysis is then used to back-calculate the yet unmeasured modulus of the XF phase from experimental deformation data, thereby providing a simple alternative to potentially complex direct measurements. This is demonstrated and validated for parallel-fiber bone tissue.