Anisotropic growth of materials

Abstract
Materials in growth have specific features such that changing their own configuration in a particular direction while re-organizing themselves to fit the surroundings. Growth can therefore be viewed as some irreversible anisotropic local structural rearrangement for which more material of the same type is squizzed in the same "particle"- entering the general theory of such rearrangements in the finite-strain framework. Accordingly, a thermodynamically admissible model of volumetric growth is contemplated which exploits the notion of material transplant (or local structural rearrangement). The associatedriving force appears to be the Mandel stress (a part of the Eshelby stress tensor or energy-momentum tensor). Anisotropy of growth is characterized by a vector field slaved to the principal directions of that tensor. The model obtained is one of anisotropic visco-elasticity in finite strains. It is applicable to self-organization or adaptation. The validity of the model is assessed in terms of (i) circumferential (monotonic) growth/resorption behavior, (ii) stress induction in a ring, and (iii) dynamic effects (repeated alternate loading) on the material growth in a cantilever beam.