A continuum model of a mixture of bone tissue and bio-resorbable material for simulating mass density redistribution in a 2d sample

The bio-mechanical phenomena occurring in bones grafted with the inclusion of artificial materials demand the formulation of mathematical models which are refined enough to describe their non-trivial behavior. In this paper reference is made to earlier works, where a 3D model was proposed and numerical examples were performed in 1D space to investigate and explain some fundamental mechanisms possible during remodeling process. Herein possible effects resulting from 2D interactions are being discovered and examined which may not be present in 1D case so more realistic situations are approached and discussed. This model was used to numerically analyze the physiological balance between the processes of bone apposition and resorption and material resorption in a plate-like sample. The specimen was constituted by a portion of bone living tissue and one of bio-resorbable material and was acted by in-plane loading conditions. A range of load magnitude was identified within which a physiological state is established. A parametric analysis was carried out to evaluate the sensitivity of the model to changes of some critical quantities within physiological ranges.