5 - Mechanics and Thermodynamics of Volumetric and Surface Growth

Abstract

We provide in this chapter a mechanical and thermodynamical basis for the modeling of volumetric and surface growth of living tissues viewed as continua undergoing changes of mass, shape and properties due to biological evolution. It is usually recognized that soft biological tissues grow by a change of specific volume or density (volumetric growth), whereas hard tissues like bone are prone to surface growth. The field equations of continuum mechanics are extended in order to account for the existing source of mass and mass flux responsible for growth. The thermodynamics of coupled irreversible phenomena is then reviewed, and evolution laws for a growth tensor in the context of volumetric growth are formulated, considering the interactions between the transport of nutrients and the mechanical forces responsible for growth. In the last part, surface growth phenomena are introduced on the basis of preliminary aspects of the differential geometry of surfaces, and further expanded in the framework of the thermodynamics of surfaces. We conclude by a presentation of extremum thermodynamic principles for growing tissues.