On a FEM model for isotropic and transversely isotropic growth in biphasic materials

Abstract

The presented continuum mechanical model describes isotropic and transversely isotropic growth in biphasic materials with focus on biological tissue. The model is capable to describe full isotropic growth, full transversely isotropic growth as well as a combination of both types. This approach is chosen to describe the most common occurring growth types, namely isotropic and transversely isotropic growth, but also to describe effects where the growth of the investigated body depends on multiple single growth effects that are difficult to distinguish among each other. For the description of growth a biphasic homogenized approach within the framework of the theory of porous media (TPM) is used. In this work we focus on the applied formulation of multiple multiplicative decoupling of the deformation gradient into elastic, growth, isotropic and transversely isotropic parts including the governing constitutive equations. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)