Fracture and non-linear response of biopolymer network with dynamic cross-linkers

Abstract

Biopolymer Networks, including cytoskeleton and hydrogels, are extremely important in living and biomaterial systems and have very similar physical properties. The mechanical behavior of biopolymer networks is computationally investigated in this study. These networks, known for their semiflexible nature and resistance to external loading, have seen various simulation methods and experimental approaches employed for their study. However, aspects such as the impact of micro-cracks on deformation and fracture response remain not fully understood. Additionally, the mechanics of slide-ring crosslinkers' movement and aggregation within the network and their effect on bulk mechanical properties are still lacking comprehensive understanding.

This research reports on a computational model that accounts for large deformations, thermal fluctuations, and forced crosslink breaking. It is discovered that micro-cracks can alter fracture paths, enhance ductility, and counterintuitively increase fracture energy. The maximum fracture resistance is achieved when crack length is a few times the network pore size, indicating a flaw-insensitive nature. The fracture energy is observed to increase with the linear stiffness of crosslinking molecules but reaches a minimum at an intermediate rotational stiffness value.

Furthermore, a theoretical formulation is established to describe the behavior of slide-ring crosslinkers within the network. These crosslinkers, treated as unbreakable and capable of random movement, are shown to significantly influence network stiffness and stress distribution upon crystallization. Slide-ring networks exhibit a lower bulk modulus under small deformations, with a more homogeneous stress distribution due to mobile crosslinkers. As deformation increases, crystallization is triggered, immobilizing most crosslinkers and substantially increasing network stiffness, a finding consistent with recent experimental observations.

The findings enhance the understanding of cytoskeletal mechanics and provide valuable insights for the development of high-performance biological materials.