How to implement constrained mixture growth and remodeling algorithms for soft biological tissues

Biological soft tissues are constantly adapting to their mechanical environment and remodel to restore certain mechanobiological homeostatic conditions. These effects can be modeled using the constrained mixture theory, that assumes degradation of material over time and the gradual replacement of extant material by newly deposited material. While this theory presents an elegant way to grasp phenomena of growth and remodeling in soft biological tissues, implementation difficulties may arise. Therefore, we give a detailed overview of the mathematical description of the constrained mixture theory and its homogenized equivalent, and present practical suggestions to numerically implement the theories. These implementations are thoroughly tested with multiple example growth and remodeling models. Results show a good correspondence between both theories, with the homogenized theory favored in terms of time efficiency. Results of a step time convergence study show the importance of choosing a small enough time step, especially when using the classical theory.