On the mechanics of solids with a growing mass

A general constitutive theory of the stress-modulated growth of biomaterials is presented with a particular accent given to pseudo-elastic soft living tissues. The governing equations of the mechanics of solids with a growing mass are revisited within the framework of finite deformation continuum thermodynamics. The multiplicative decomposition of the deformation gradient into its elastic and growth parts is employed to study the growth of isotropic, transversely isotropic, and orthotropic biomaterials. An explicit representation of the growth part of the deformation gradient is given in each case, which leads to an effective incremental formulation in the analysis of the stress-modulated growth process. The rectangular components of the instantaneous elastic moduli tensor are derived corresponding to selected forms of the elastic strain energy function. Physically appealing structures of the stress-dependent evolution equations for the growth induced stretch ratios are proposed.