A second gradient continuum model accounting for some effects of micro-structure on reconstructed bone remodelling

We propose a second gradient, two-solids, continuum mixture model with variable masses to describe the effect of micro-structure on mechanically-driven remodelling of bones grafted with bio-resorbable materials. A one-dimensional numerical simulation is addressed showing the potentialities of the proposed generalized continuum model. In particular, we show that the used second gradient model allows for the description of some micro-structure-related size effects which are known to be important in hierarchically heterogeneous materials like reconstructed bones. Moreover, the influence of the introduced second gradient parameters on the final percentages of replacement of artificial bio-material with natural bone tissue is presented and discussed.