Modelling framework for mass-growth III: Isochoric growth

• This paper complements and completes the non-isotropic mass-growth modelling framework presented in [1] and [2].
• It presents a relevant formulation for isochoric deformation processes that exhibit features of simultaneous elastic and plastic mass-growth.
• It follows is slightly different and more general modelling route to that followed in Soldatos [2].
• It handles successfully the explicit or a hidden relationship that may exist between the deformation gradient and plastic flow tensors.
• Purely pseudo-elastic and purely pseudo-plastic isochoric mass-growth models can be obtained as particular cases.

Mass-growth is usually perceived as a non-isochoric process, but classes of soft tissue that exhibit incompressible or nearly incompressible in vitro behaviour may have gone through growth stages which are isochoric or nearly isochoric. The present paper aims thus to complement and complete the non-isochoric mass-growth modelling framework presented in [1] and [2] by presenting a relevant formulation for isochoric deformation processes that exhibit features of simultaneous elastic and plastic mass-growth. The refined modelling route that is followed is slightly different, and more general to that followed in [2], to which, however, is also applicable. Because mass density and stress levels are expected to increase faster than they would in analogous non-isochoric mass-growth situations, purely pseudo-elastic or purely pseudo-plastic stages of isochoric mass-growth are rather unlikely to alternate in the manner implied in [1] for their non-isochoric counterparts. Purely pseudo-elastic and purely pseudo-plastic isochoric mass-growth models can however still be obtained as particular cases of the present formulation. These issues as well as additional features that characterise the present model are detailed and clarified further through the complete, closed form solution of a particular, example problem application in which the mass density and the shape of the growing continuum are subjected to continuous time change.