A new approach to the simulation of microbial biofilms by a theory of fluid-like pressure-restricted finite growth

In general, the term ’growth’ characterises the process by which a living body increases in size by addition of mass. Living matter grows in various different ways, triggered by genetic and biological factors. In addition, the configuration of the grown body in space depends on its interaction with the environment at the boundaries. In this paper, we deal with mechanical constraints on growth at the boundary of the body. Particularly, we present a model for growth such that residual stresses resulting from an isotropic deposition of new material are continuously relieved and that depends on the hydrostatic pressure acting on the material. As an example for this pressure-restricted fluid-like type of growth, we consider microbial biofilms growing between rigid obstacles in geometrically confined environments. The presented concept unites two classical constitutive formulations of large strain viscoelasticity and finite growth. The model was implemented into a finite element framework to illustrate its performance in several benchmark problems.