Multiporoelasticity of Hierarchically Structured Materials: Micromechanical Foundations and Application to Bone

Abstract

We here extend the theory of microporomechanics by Dormieux et al. to multiple pore spaces. As an application, we reveal, on the basis of a recently validated multiscale elastic model for bone tissues by Fritsch and Hellmich, the effects of multiple pore pressures in various, scale-separated pore spaces, on the overall behavior of the multiporous composite material. Thereby, our focus is on the lacunar pore space, and on its interplay with the pore spaces found further below: not only those between the mineral crystals (of some 10 nm characteristic pore size) but also those of the collagen molecules building up (micro-)fibrils (with a little more than 1 nm distance between these molecules). Our results clearly show that the interplay between pore pressure and skeleton deformation depends strongly on the loading direction and on the characteristic size of the pores—hence, we can conclude that the consideration of these strongly hierarchical and anisotropic effects in whole-organ simulations including fluid...