From the FENE Model to Polymer Rupture

Abstract

In this study, we propose a novel polymer rupture model that focuses on the transition from elastic to softening deformation under mechanical stimuli. Starting with the end-to-end vector approach and drawing from the finitely extensible nonlinear elastic (FENE) model, we develop a criterion for polymer breakage. This model improves upon previous approaches that lacked clear mechanical rupture criteria. The method involves addressing singularities in the FENE model by introducing the \(\gamma \) term in the second-order expansion of spring deformation, allowing for a transition from elastic to softening deformation. As the force diminishes, rupture occurs at \(Q > Q_0 / \sqrt{|\gamma |}\). Results show that the model effectively simulates energy dissipation during the breakdown process, providing insights into polymer behavior in turbulent fluid dynamics.