$\newcommand{\Dev}{\operatorname{Dev}}$ $\newcommand{\dev}{\operatorname{dev}}$ $\newcommand{\grad}{\operatorname{grad}}$ $\newcommand{\divg}{\operatorname{div}}$ $\newcommand{\Ei}{\operatorname{Ei}}$ $\newcommand{\tr}{\operatorname{tr}}$

This type of material [5] implements a mechanism for multigenerational interstitial growth of solids whereby each growth generation $\gamma$ has a distinct reference configuration $\mathbf{X}^{\gamma}$ determined at the time $t^{\gamma}$ of its deposition. Therefore, the solid matrix of a growing material consists of a multiplicity of intermingled porous bodies, each representing a generation $\gamma$ , all of which are constrained to move together in the current configuration $\mathbf{x}$ . The deformation gradient of each generation is $\mathbf{F}^{\gamma}=\partial\mathbf{x}/\partial\mathbf{X}^{\gamma}$ . The first generation ($\gamma=1)$ is assumed to be present at time $t^{1}=0$ , therefore its reference configuration is $\mathbf{X}^{1}\equiv\mathbf{X}$ and its deformation gradient $\mathbf{F}^{1}=\partial\mathbf{x}/\partial\mathbf{X}^{1}$ is equivalent to $\mathbf{F}=\partial\mathbf{x}/\partial\mathbf{X}$ . Each generation's reference configuration $\mathbf{X}^{\gamma}$ has a one-to-one mapping $\mathbf{F}^{\gamma1}=\partial\mathbf{X}^{\gamma}/\partial\mathbf{X}^{1}$ with the master reference configuration $\mathbf{X}^{1}$ , which is that of the first generation. This mapping is postulated based on a constitutive assumption with regard to that generation's state of stress at the time of its deposition. In the current implementation, the newly deposited generation is assumed to be in a stress-free state, even though the underlying material is in a loaded configuration. Therefore, the mapping between generation $\gamma$ and the first generation is simply $\mathbf{F}^{\gamma1}=\mathbf{F}^{1}\left(\mathbf{X}^{1},t^{\gamma}\right)\equiv\mathbf{F}\left(\mathbf{X},t^{\gamma}\right)$ . In other words, when generation $\gamma$ first comes into existence, its reference configuration is the current configuration at time $t^{\gamma}$ . Note that $\mathbf{F}^{\gamma1}$ is a time-invariant (though not necessarily homogeneous) quantity that is determined uniquely at the birth of a generation.