A chemo-mechanical model coupling damage and mechanofluorescence for tough interpenetrating elastomers

Peng Sun

doi:10.1016/j.jmps.2026.106627

A chemo-mechanical model coupling damage and mechanofluorescence for tough interpenetrating elastomers

2026-04-09

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DOI：10.1016/j.jmps.2026.106627

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Abstract

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Mechanochemical probes have emerged as powerful tools for directly visualizing stress distribution and damage evolution in polymeric materials. Recent studies have successfully embedded rhodamine-based mechanophores into multiple network elastomers to enable high-resolution mechanofluorescent signaling. However, cyclic loading experiments reveal distinct fluorescence response across different loading cycles, which indicate a strong coupling between mechanofluorescent signals and the progressive damage within polymer networks. Motivated by these findings, we develop a chemo-mechanical model that quantitatively captures the mechanofluorescent behavior. We first introduce an extended-Langevin model for the behavior of single chain with deformable bonds. The free energy density of the first network is derived by considering chains with varying segment lengths, while a kinetic damage evolution law is introduced to account for progressive network degradation. The free energy density of multiple network elastomers is formulated as the combined contribution of a hyperelastic matrix network and a first network undergoing damage evolution. We further incorporate the chemical kinetics of ring-opening mechanophores into the theoretical framework. Activation of mechanophores occurs when the chain force exceeds a critical threshold, while deactivation occurs upon a reduction or removal of the force. Through parametric analysis, we demonstrate the key factors that strongly influence mechanochemical behavior. The model is then validated against experimental results from mechanofluorescent multiple network elastomers, accurately capturing both mechanical and fluorescent response in single to triple network elastomers under cyclic loading. Notably, the model reproduces stress softening and the increase in critical activation stretch caused by accumulated damage. The model is further implemented for finite element analysis to predict cyclic mechanochemical response under inhomogeneous deformation conditions, with predictions showing quantitative consistency with experimental spatial fluorescence distribution.

Keywords:

mechanochemical model

damage evolution

mechanofluorescence

interpenetrating elastomers

chemo-mechanical coupling

A chemo-mechanical model coupling damage and mechanofluorescence for tough interpenetrating elastomers

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