An Anisotropic Micro-Sphere Approach Applied to the Modelling of Soft Biological Tissues

Abstract

A three-dimensional model for the simulation of anisotropic soft biological tissues is discussed. The underlying constitutive equations account for large strain deformations and are based on a hyper-elastic form. As various soft biological tissues are nearly incompressible, we adopt the classical volumetric-isochoric split of the strain energy density. While its isotropic part is chosen to take a standard neo-Hookean form, its anisotropic part is determined by means of the so-called micro-sphere model. In this regard, physically sound one-dimensional constitutive models – as for instance the worm-like chain model – can be used and straightforwardly be extended to the three-dimensional case. As a key aspect, the micro-sphere model is extended to further capture remodelling. Such deformation-induced anisotropy is introduced by setting up evolution equations for the integration directions used to perform numerical integrations on the unit-sphere. The particular model proposed captures orthotropic material behaviour and additionally accounts for saturation effects combined with a visco-elasticity-type time-dependent anisotropy evolution.