LAUSR

Abstract We develop in this contribution models for material accretion and surface growth in the framework of the thermodynamics of irreversible phenomena. Accretion is a general situation in physics, encompassing phenomena like masonry, gravitational accretion, chemical vapor deposition, or volcanic and sedimentary rock formation. Surface growth in a biological context results from the incremental accretion of new tissue onto the boundary of a solid body, due to the activity of generating cells which produce new tissue, this last process deserving the coinage surface growth. The classification into pure accretion occurring without growth and surface growth is concomitant to the definition of the growth velocity as the difference between the total velocity and the accretion velocity, this last quantity being defined as the velocity of the surface or interface occupied by the set of generating cells in a biological context. Moving (resp. fixed) generating cells or material points correspond to the respective situations of surface growth in a biological context and to accretion in physics. Based on this classification, we first analyze the situation of pure surface growth occurring in an elastic solid body, under the umbrella of the thermodynamics of irreversible phenomena. The situation of mass accretion of a spherical domain is given as an illustration. This framework is next enlarged to material accretion accompanied by surface growth, whereby an evolution law for the growth velocity gradient is obtained versus a conjugated driving force. Both problems of accretion and surface growth are coupled through the accretion velocity. Numerical simulations are performed in the biomechanical context of bone external remodeling to illustrate the general situation of combined accretion and surface growth.