A Transient Microsphere Model for Nonlinear Viscoelasticity in Dynamic Polymer Networks

Abstract

Viscoelastic material behavior in polymer systems largely arises from dynamic topological rearrangement at the network level. In this paper, we present a physically motivated microsphere formulation for modeling the mechanics of transient polymer networks. By following the directional statistics of chain alignment and local chain stretch, the Transient Microsphere Model (TMM) is fully anisotropic and micro-mechanically based. Network evolution is tracked throughout deformation using a Fokker-Planck equation which incorporates the effects of bond creation and deletion at rates that are sensitive to the chain-level environment. Using published data, we demonstrate the model to capture various material responses observed in physical polymers.

Rate-Dependent Damage Mechanics of Polymer Networks with Reversible Bonds

“…We finally note that our usage of a first-order kinetic law, with constant rates of k a and k d , does not account for the force sensitivity of bond lifetime in many physical systems . The model may therefore be supplemented by including a functional form of k d on the force f in the chain as per previous works . Relaxing some of these assumptions is expected to yield better fittings for the experimental comparisons presented in this work.…”

“…We emphasize the intention of this work to provide a qualitative understanding of the governing physics outlined in Section and note that a more sophisticated numerical strategy could mitigate this. For instance, reducing the model to the domain of a microsphere ,, could significantly reduce computational cost and open the possibility for implementation in finite element method models. We finally note that our usage of a first-order kinetic law, with constant rates of k a and k d , does not account for the force sensitivity of bond lifetime in many physical systems .…”

“…Relaxing some of these assumptions is expected to yield better fittings for the experimental comparisons presented in this work. In particular, the Mullins-like effect observed in Figure b that was not captured by this model has been explained by other researchers by network alteration (reflecting the changes of non-affine deformation) as well as nonlinear viscoelasticity …”

“…This is true for most physical systems and has been discussed in previous works . We particularly note that this inequality remains satisfied when considering the sensitivity of bond detachment to external forces, which is explicitly discussed in the context of the TNT by Lamont and Vernerey …”

Thermosensitive P(AAc‐co‐NIPAm) Hydrogels Display Enhanced Toughness and Self‐Healing via Ion–Ligand Interactions

“…This suggested slip bond behavior is commonplace [44] and supported by the results of Figure 2F which also displays an inverse relation between k d and stress magnitude. [45,46] To further explore the dissipative effects of reversible bond dissociation, we also evaluated the mechanical response of D h-0.033-Y hydrogels undergoing cyclic uniaxial loading experiments with no recover time between cycles. Figure 5A shows the engineering stress-strain response of a D h-0.033-2 hydrogel undergoing cyclic loading to different peak strains.…”