Stress relaxation in fiber networks via force-dependent stochastic severing

Fiber networks contribute to the mechanical stability of various biological systems, from cells to tissues. Such systems have been modeled by networks of springs or fibers that exhibit rigidity transitions as a function of either connectivity or applied strain. For a fiber network under constant applied strain, severing can reduce the connectivity and destabilize an initially rigid structure. Here, we investigate stress relaxation in spring and fiber networks in the presence of stochastic, force-dependent severing. A computational model to predict stress relaxation with mechanochemical feedback of stress on severing is developed. We also examine the effects of severing on the network topology and onset of rigidity transition. Using 2D triangular lattice-based computer simulations, we explore different limits of the feedback and demonstrate the shift in the onset of rigidity depending on the limit. The limit of tension-suppressed severing delays stress relaxation and shifts the transition into the bending-dominated regime to lower-than-expected connectivity. In contrast, tension-enhanced severing accelerates relaxation and shifts the transition to higher-than-expected connectivity. It is also found that the magnitude of this shift depends on the applied shear strain and the strength of the feedback. Our theoretical approach clarifies some microscopic aspects of these phenomena. Understanding the impact of such feedback mechanisms can provide valuable insights into designing systems by tuning the feedback to the desired response.