Modeling the Mechanics of Semiflexible Biopolymer Networks: Non-affine Deformation and Presence of Long-range Correlations

Abstract

An intertwined network of fibers forms the microstructure of many biological materials and defines their mechanical properties. Depending on the properties of individual fibers, from mechanics point of view, these fibrous materials can be considered to behave as semiflexible networks or flexible networks. While the behavior of flexible networks has been studied thoroughly, the mechanics of semiflexible networks is a less developed subject. In semiflexible networks, the filaments resist the external stresses by storing energy in both bending and axial modes of deformation. Their deformation field is non-affine and has long range correlations within a certain range of scales of observation. Due to the increasing interest in understanding the mechanical and rheological properties of complex systems such as the cell cytoskeleton and connective tissue, a growing interest was manifested in characterizing the mechanics of the semiflexible networks in the recent years. This chapter discusses recent advances in the field of semiflexible random fiber networks, including the quantification of their non-affine deformation and methods for solving boundary value problems on fibrous domains with intrinsic long range correlations.