A bone remodeling model involving two mechanical stimuli originated from shear and normal load conditions within the 3D continuum mechanics framework

We propose a three-dimensional macroscopic continuum model designed to predict the remodeling phenomenon of bone tissue. In the proposed model, we focus on the evolution of two crucial stiffness parameters: the bulk and shear moduli. These parameters independently adapt to the mechanical demands to which bone tissue is subjected, mainly to withstand hydrostatic and deviatoric deformations. These mechanical stimulations influence the activity of bone cells, leading to changes in bone structure and strength and, in turn, the above-mentioned moduli. The formulation is simplified, serving as an initial step towards a more comprehensive modeling approach. The evolution of these stiffness parameters is proposed based on an energetic argument to describe the functional adaptation process. Numerical experiments, conducted on a cylindrical specimen resembling a femur, demonstrate the feasibility of modeling the bone remodeling process with distinct evolutions for multiple material parameters, in contrast to the conventional approach that permits only one-parameter evolution.