Modeling semi-flexible biopolymer networks with geometrically exact, non-linear isogeometric beams

Abstract

Biopolymers are an important class of materials that comprise many biological tissues. Their semi-flexible nature sets them apart from most synthetic polymers. Thus, the development of material-specific models is an important step toward understanding their structure-function relationship. This, in turn, will enable us to understand biological tissues such as heart valves, arteries, and skin. Here we propose and test the use of geometrically-exact, nonlinear isogeometric beams and beam assemblies to model semi-flexible polymer networks. Beyond establishing and validating this modeling framework, we demonstrate its potential by exploring the deformations of individual fibers and of 3D semi-flexible biopolymer networks. We do so in networks of straight and undulated fibers and find that fiber geometry significantly alters the networks’ macro-mechanics. Additionally, we find that fibers undergo a well-preserved sequence of loading modes. Specifically, fibers first reorient and bend and are then uniaxially stretched. We further showcase our framework by successfully comparing a fibrin pure shear experiment against our model predictions. We believe that our modeling framework will be useful in continuing the investigation of the structure-function relationships of semi-flexible biopolymer networks and will thus provide insight into the mechanics of biological tissues.