A kinematically and thermodynamically consistent volumetric growth model based on the stress-free configuration

A continuum volumetric growth theory is presently elaborated based on the stress-free configuration. The total deformation gradient is the composition of a growth mapping followed by an elastic mapping ensuring the compatibility of the body. A measure of the growth rate fully lying in the stress-free configuration is elaborated, and the balance of momentum accounting for mass changes due to growth is written in the same configuration, highlighting measures of kinematic incompatibilities. An Eshelby stress is identified as the driving force for growth, in the sense that it appears as the true dissipative thermodynamic force conjugated to the growth rate. Examples of incompatible cylindrical growth with residual stress generation and tumor growth with mechanics coupled to diffusion of nutrients illustrate the proposed theory.