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Theory Manual Version 3.6
 Subsection 2.8.4: Simple Solid Mixtures Up Section 2.8: Constrained Reactive Mixture of Solids Subsection 2.8.6: Prescribed Pre-Stretch 

2.8.5 Multigenerational Interstitial Growth

Multigenerational interstitial growth mechanics may be modeled using a reactive mixture of constrained solids as described in [7]. In this framework it is assumed that a porous solid matrix may gain mass via interstitial growth, such that the porosity of the solid decreases with increasing solid mass content. The history of growth is discretized temporally into generations such that the mass added in the time interval has a reference configuration . This model assumes that each generation gets deposited into the existing mixture in a stress-free state. This can be achieved by adopting the constitutive assumption that . In other words, the reference configuration of generation is the current configuration of the solid mixture at time . An alternative form of this constitutive model is that while the new generation is being deposited, or equivalently according to eq.(2.8.1-2).
The underlying assumption of multigenerational growth is that evolves for each generation either due to load-induced deformations or deformations produced by swelling processes, such as cell growth or Donnan swelling.
This type of multigenerational growth material is implemented in FEBio as “multigeneration” for mixtures of elastic solids, and as “multiphasic-multigeneration” for reactive multiphasic mixtures whose solid constituent is a multigenerational growth material. In this type of material the user needs to prescribe the generation birth times and the properties of the material of each generation . The code automatically prescribes based on the constitutive model given above, for each generation . For example, one may use a material model whose response depends on the evolving composition of that generation. The composition may evolve either due to chemical reactions modeled in a multiphasic framework, or by associating a user-defined load curve with . Thus, the material properties (and the stress response) of generation need not remain constant over the generation time interval , even though remains constant during that generation.
When the growth process is negative ( ), it implies that the solid constituent is losing mass (solid resorption); this loss of mass terminates when . A material model that depends on may exhibit evolving material properties during this resorption process until that generation produces zero stress when .
As a result of these evolving growth processes, this multigeneration mixture may exhibit residual stresses.
 Subsection 2.8.4: Simple Solid Mixtures Up Section 2.8: Constrained Reactive Mixture of Solids Subsection 2.8.6: Prescribed Pre-Stretch