A statistical theory for polymer elasticity: from molecular kinematics to continuum behavior

TL;DR

This paper develops a new statistical Hamiltonian-based model for polymer elasticity that accurately predicts macroscopic behavior from molecular kinematics without phenomenological assumptions.

Contribution

It introduces a unified statistical framework linking chain segment kinematics to continuum behavior using a novel Hamiltonian, improving predictive accuracy.

Findings

Enhanced hyperelastic response predictions for elastomers.

Minimal parameter model grounded in physical principles.

Better alignment with experimental data compared to existing models.

Abstract

Predicting the macroscopic mechanical behavior of polymeric materials from the micro-structural features has remained a challenge for decades. Existing theoretical models often fail to accurately capture the experimental data, due to non-physical assumptions that link the molecule kinematics with the macroscopic deformation. In this work, we construct a novel Hamiltonian for chain segments enabling a unified statistical description of both individual macromolecular chains and continuum polymer networks. The chain kinematics, including the stretch and orientation properties, are retrieved by the thermodynamic observables without phenomenological assumptions. The theory shows that the chain stretch is specified by a simple relation via its current spatial direction and the continuum Eulerian logarithmic strain, while the probability of a chain in this spatial direction is governed by the new Hamiltonian of a single segment. The model shows a significantly improved prediction on the hyperelastic response of elastomers, relying on minimal, physically-grounded parameters.