A contribution to the mechanics and thermodynamics of surface growth. Application to bone external remodeling

The surface growth of biological tissues is presently analyzed at the continuum scale of tissue elements, adopting the framework of the thermodynamics of surfaces. Growth is assumed to occur in a moving referential configuration (called the natural configuration), considered as an open evolving domain exchanging mass, work, and nutrients with its environment. The growing surface is endowed with a superficial excess concentration of moles, which is ruled by an appropriate kinetic equation. From a thermodynamic framework of surface growth, the equilibrium equations are derived in material format from a suitable thermodynamic potential, highlighting the material surface forces for growth based on a surface Eshelby stress. Those forces depend upon a surface Eshelby stress, the curvature tensor of the growing surface, the gradient of the chemical potential of nutrients, and a surface force field. Application of the developed formalism to bone external remodeling highlights the interplay between transport phenomena and generation of surface mechanical forces. The model is able to describe both bone growth and resorption, according to the respective magnitude of the chemical and mechanical contributions to the material surface driving force for growth. (C) 2011 Elsevier Ltd. All rights reserved.