A multi-mechanism model for damage and dissipation in filled elastomer networks

Filled elastomers exhibit complex mechanical behaviors under multiaxial and cyclic loading, driven by a combination of nonlinear elasticity, viscoelastic effects, filler network evolution, and molecular-scale damage mechanisms. Accurately capturing these coupled phenomena remains a major challenge for constitutive modeling, particularly when accounting for anisotropy, loading history, and filler-induced effects. In this work, a multi-mechanism, physically-based visco-hyperelastic model is developed to predict the history-dependent response of filled elastomers. The approach relies on a network decomposition strategy that distinguishes between pure and filled polymer networks, each comprising elastic and viscous elements. The filler cluster network explicitly models local strain amplification induced by polymer-filler interactions and its progressive evolution with damage. The model integrates key microstructural mechanisms: chain scission, cluster-chain debonding, filler cluster breakdown, chain viscosity, and interfacial sliding viscosity. Chain rupture processes are treated as energy-activated events, while polymer entanglements are captured through a tube-based framework, and filler network rearrangements are modeled via dynamic flocculation theory. The predictive capabilities of the multi-mechanism model are assessed against a comprehensive experimental dataset on a carbon-filled elastomer system across various filler concentrations, covering multiaxial monotonic and cyclic loading conditions. Particular emphasis is placed on the effects of pre-stretching and directional reloading on anisotropic softening and energy dissipation. Beyond reproducing stress-strain behavior, the model also captures the direct link between mechanical degradation and the evolution of electrical resistivity. This comprehensive framework advances the modeling of filled elastomer networks by explicitly capturing the coupled multi-mechanism interactions - including cluster-chain debonding, cluster damage, chain scission, and interfacial viscous sliding - that govern the interplay between microstructural evolution, anisotropy, and mechanical energy dissipation across diverse loading paths.