[Paper Review] From Connectivity to Rupture: A Coarse-Grained Stochastic Network Dynamics Approach to Polymer Network Mechanics

Shaswat Mohanty, Wei Cai|arXiv (Cornell University)|Feb 8, 2026

Polymer composites and self-healing0 citations

TL;DR

The paper introduces CGSND, a network-based coarse-grained framework that models deformation and rupture in polymer networks using force-controlled bond failure, and validates it against CGMD simulations.

ABSTRACT

We introduce a coarse-grained stochastic network dynamics (CGSND) framework for modeling deformation and rupture in polymer networks. The method replaces explicit molecular dynamics (MD) or coarse-grained molecular dynamics (CGMD) with network-level evolution rules while retaining chain entropic elasticity and force-controlled bond failure. Under uniaxial loading, CGSND reproduces the characteristic nonlinear stress--stretch response of elastomeric networks, including a well-defined ultimate tensile strength and post-peak softening due to progressive bond rupture. Comparison with coarse-grained molecular dynamics (CGMD) simulations shows that CGSND captures the qualitative form of the stress response and the onset of catastrophic damage despite its rate-independent formulation. Analysis of rupture kinetics reveals a pronounced peak in the bond-breaking hazard rate near the ultimate tensile strength in both approaches. In addition, the distribution of broken segment lengths remains statistically indistinguishable from the initial network, indicating that rupture is not biased toward short or long chains. Finally, the evolution of the Gini coefficient of bond force magnitudes reveals strong force localization preceding failure. These results demonstrate that CGSND provides a computationally efficient and physically interpretable framework for connecting force localization and rupture kinetics to macroscopic failure in polymer networks.

Motivation & Objective

• Bridge the gap between microscopic chain mechanics and macroscopic failure in polymer networks while reducing computational cost.
• Retain entropic elasticity and force-controlled rupture within a graph-based network representation.
• Characterize rupture kinetics and load redistribution via hazard rates and force localization metrics.
• Demonstrate that network-level dynamics reproduce key nonlinear elastic and failure features seen in molecular simulations.

Proposed method

• Represent cross-linked polymer networks as weighted graphs with nodes as beads and edges carrying strand-length weights.
• Use affine loading and an inverse Langevin-based bond force law to capture entropic stiffening and force amplification.
• Implement a force-controlled bond rupture criterion with a fixed cut-off force to progressively remove bonds.
• Compute macroscopic stress via a bulk virial formulation and map to MPa using a thermal stress scale.
• Define bond rupture hazard rate h(lambda) as the stretch-resolved instantaneous rupture probability per initial bond.
• Quantify load localization with the Gini coefficient of instantaneous bond force magnitudes.

Experimental results

Research questions

• RQ1 Can a coarse-grained stochastic network dynamics (CGSND) framework reproduce the qualitative stress–stretch response of elastomeric polymer networks seen in CGMD?
• RQ2 How do rupture kinetics, including hazard rates and rupture type (cross-links vs backbone bonds), compare between CGSND and CGMD under uniaxial loading?
• RQ3 Does force localization (Gini coefficient) precede and characterize macroscopic failure in CGSND as in molecular simulations?
• RQ4 Is rupture in CGSND biased toward particular segment lengths, or is it a cooperative, network-mediated process?

Key findings

• CGSND reproduces the qualitative nonlinear stress–stretch curve with a well-defined ultimate tensile strength and post-peak softening similar to CGMD.
• Rupture hazard rates peak near the ultimate tensile strength in both CGSND and CGMD, indicating a kinetic transition at failure onset.
• Distributions of broken segment lengths remain statistically close to the initial network distribution, showing rupture is not biased toward short or long chains.
• CGSND reveals strong force localization prior to failure, evidenced by a peak in the Gini coefficient around the ultimate tensile strength.
• CGSND is computationally efficient and provides mechanistic links between force localization, rupture kinetics, and macroscopic response, despite omitting inertial and thermal dynamics.