A triphasic model of transversely isotropic biological tissue with applications to stress and biologically induced growth

A triphasic model (solid, interstices filled with water containing nutrients) is proposed for the phenomenological description of transversely isotropic saturated biological tissues including the phenomena of growth. This is done within the framework of a macro-mechanical description based on the Theory of Porous Media (TPM). Thereby, the constitutive equation of growth is determined by the state of stress and the local proportion of nutrients responsible for the mass exchange. The transversely isotropic behavior of the solid influences both the stress response and the internal fluid permeability, which is considered using an invariant formulation of the Helmholtz free energy and transversely isotropic permeability functions. After presenting the developed framework of the calculation concept including the representation of the governing weak formulations of the equations for large deformations, some representative numerical examples are examined.