The insight of mixtures theory for growth and remodeling

The emergence of residual stress as due to growth and remodeling of soft biological tissues is considered in the framework of the mixture theory. The focus is on mixtures composed by one elastic solid component and several fluid ones. It is shown that the standard theory is unable to predict residual stresses unless enriched by a suitable descriptor of growth. Both the introduction of a dependence of the free energy on the density of the solid component and the Kroner-Lee multiplicative decomposition of the gradient of deformation are effective in this respect, with different levels of generality. When adopting a multiplicative decomposition of the tensor gradient of deformation, thermodynamical arguments suggest constitutive laws for the evolution of the growth tensor that point out the role of the concentration of fluid species in driving the emergence of residual stress thanks to inhomogeneous growth.