Numerical modelling of inhomogeneous volume growth
Growth in living bodies is understood as the increase of mass and volume during their development. Depending on the directions in which volume growth takes place, the growth process can be equal in every direction (isotropic growth) or can appear with preferred directions (anisotropic growth). When loads or constraints interact with the body during growth, some growing bodies change their growth behaviour. More specifically, these bodies grow in a direction inducing a lower energy state, as if their growth behaviour is maintained. With this statement, one can find isotropic growing bodies that grow anisotropically, or anisotropically growing bodies that change their direction and properties due to the existence of loads/constrains.
Using a phenomenological point of view, these growing bodies seem to change their growing direction when boundaries constrain them. Hereby, it can be considered that during growth the body behaves like a viscoelastic fluid while the mechanical behaviour is typical of solid materials. The changes on the growth directions are described as the flow of a viscoelastic material by means of a flow rule. Some restrictions have to be imposed in the flow rule due to the solid behaviour of those materials and the consideration of a positive growth (the addition of material is always greater or equal to zero). In a micro scale, the reorientation process can be seen as an adaptive process of cell division in the direction of the elastic deformations or stresses.
The use of numerical models for the simulation of growth phenomena has been increasing in popularity in the last two decades. The prediction of the shape in growing bodies considering morphogenesis and reorientation of volume growth is a challenging objective in biomechanics. Growth models implemented into nonlinear finite element approaches allows the use of complex geometries and boundary conditions in the simulations. Therefore, the development of finite element models for analysis of growth phenomena presents a flexible tool for studies involving adaptive, morphological changes and reorientation in volume growth processes.
