A micromechanically motivated model for the viscoelastic behaviour of soft biological tissues at large strains

Abstract

In this contribution, a non-linear viscoelastic anisotropic model for soft biological tissues is presented. The viscoelastic behaviour of these materials is explained by micromechanical considerations regarding the interplay between collagen fibres and the surrounding ground substance. The model is based on a multiplicative decomposition of the fibre stretch into a part relating to the straightening of the crimped fibres and a part describing the stretch in the fibre itself. The actual structural state of the fibres is reflected by internal variables. Including a non-uniform distribution of these fibres, the anisotropic three-dimensional constitutive equations are obtained by integration over the unit sphere. The model holds for large strain problems and is illustrated by application to arterial tissue.