An enhanced version of a bone remodelling model based on the continuum damage mechanics theory.

The purpose of this work is to propose an enhancement of Doblaré and García's internal bone
remodelling model based on the continuum damage mechanics theory. In their paper, they
stated that the evolution of the internal variables of the bone microstructure, and its incidence
on the modification of the elastic constitutive parameters, may be formulated following the
principles of Continuum Damage Mechanics, although no actual damage was considered. The
resorption and apposition criteria (similar to the damage criterion) were expressed in terms of
a mechanical stimulus. However, the resorption criterion is lacking a dimensional consistency
with the remodelling rate. We here propose an enhancement to this resorption criterion,
insuring the dimensional consistency while retaining the physical properties of the original
remodelling model. We then analyse the change in the resorption criterion hypersurface in the
stress space for a 2D analysis. We finally apply the new formulation to analyse the structural
evolution of a 2D femur. This analysis gives results consistent with the original model but
with a faster and more stable convergence rate.