A Tight Knot Model of Elastomers Undergoing Deformation for Exploring Possible Contractions of Entanglements

The network structure and topology of elastomers, as well as the possible contractions of entanglements after deformation, have long been a concern for people. This paper presents a statistical thermodynamic model based on tight knot theory and the Lhuillier distribution methodology to investigate the post‐deformation conformational contraction and entanglement compaction in elastomeric materials. This study suggests that the complex network topology and entanglement of deformed elastomers are key factors leading to their nonlinear mechanical behavior. By constructing a free energy function and analyzing chain conformational distributions under tight knots, the authors derive the free energy density and constitutive equations for tightly entangled chains. Key parameters such as the flat tight exponent are shown to significantly influence mechanical performance and the network topology, with higher tight exponent values correlating with enhanced load‐bearing capacity at small deformations and strain softening at large deformations. The model's validity is confirmed through comparisons with experimental data from literature, demonstrating its ability to predict stress–strain behavior, including strain softening and hardening phenomena based on topological structure.