A thermodynamic-based principle for accretion phenomena applied to the modeling of bone external remodeling

Unlike inactive systems, living biological systems have the advantage of being able to adapt to their environment through growth. Growth is a phenomenon unique to biological tissues, which is mainly driven by accretion processes, whereby new living tissues are added only on the surface of the growing body, due to the action of generating cells. The aim of this contribution is to develop a model for material accretion in the context of the thermodynamics of continuous media. A relation between the accretion velocity and a conjugated driving force based on Eshelby stress tensor is derived from the optimum condition of the zero thermodynamic potential. Numerical simulations are subsequently carried out in the biomechanical context of bone external remodeling to elucidate the apposition of bone mineral onto the surface of proximal femur samples subjected to physiological loads.