Transient Network at Large Deformations: Elastic⁻Plastic Transition and Necking Instability

Area of Science:

• Materials Science
• Polymer Physics
• Rheology

Background:

• Transient networks are characterized by dynamic crosslinks that break and reform.
• Finite chain extensibility is crucial for describing large deformations in these materials.
• Hyperelasticity models, like the Gent model, are empirical descriptions of large deformation behavior.

Purpose of the Study:

• To develop a general theory for the mechanical response of transient networks accounting for finite chain extensibility and crosslink dynamics.
• To derive the constitutive relation for arbitrary deformations.
• To analyze the influence of strain rate versus crosslink breakage rate on material behavior.

Main Methods:

• Theoretical investigation of transient network mechanics.
• Incorporation of the Gent model for hyper-elasticity.
• Derivation of analytical expressions for elastic energy and constitutive relations.
• Analysis of uniaxial tensile strain under varying strain rates and crosslink breakage rates.

Main Results:

• The mechanical response is dictated by the ratio of strain rate to crosslink breakage rate.
• At low strain rates (relative to breakage rate), the network exhibits plastic flow beyond a yield point.
• At high strain rates, the network behaves elastically.
• A transition region exists where elastic and plastic regions coexist, leading to necking instability.
• In dual transient networks, the component with the lower breakage rate governs the overall deformation.

Conclusions:

• The interplay between strain rate and crosslink dynamics critically determines the mechanical response of transient networks.
• The developed theory accurately predicts elastic, plastic, and transitional behaviors, including necking.
• The behavior of dual transient networks is dominated by the network with slower crosslink dynamics.