Extremum principles for biological continuous bodies undergoing volumetric and surface growth

Abstract

Abstract. The volumetric and surface growth of continuum solid bodies is considered, in the framework of the thermodynamics of open systems exchanging mass, work and chemical species (nutrients) with their environment. More specifically, we address the issue of setting up extremum principles for such growing bodies. A general three-field variational principle is set up, based on the so-called zero potential, which is a byproduct of the grand potential. The stationnarity conditions of those potentials deliver balance laws for generalized volumetric and surface Eshelby tensors, leading further to the identification of the material forces for growth.