ABSTRACT
Constitutive equations for elastic-growing tissues have so far made use of the free energy per reference volume of the existing material, as if growth had no direct effect on this entity, e.g., Lubarda and Hoger. The free energy and growth rate law of elastic solids are introduced in a format close to that developed for elastic-growing solids, so as to facilitate comparison between the formulations and the quantitative mechanical responses to the boundary value problems. In other words, while the constitutive equations for the elastic-growing solids are motivated by the dissipation inequality, no such a goal is pursued in building the constitutive equations for the elastic solids. Here, both elastic solids and elastic-growing solids are addressed: the deformation gradient admits a multiplicative decomposition into an elastic transformation and a growth transformation, and the thermodynamic state includes, besides the stress or the elastic strain, a scalar entity and a tensor.
