Thermodynamic topological population mechanics for rate-dependent deformation and rupture precursors in entangled polymers

초록

Entangled polymeric solids and entangled polymer liquids exhibit rate- and mode-dependent deformation mechanisms that are difficult to represent with scalar damage or single-conformation models. Shear can produce stress overshoot and loss of load-bearing topology, whereas extension can produce strain hardening and topological lock-up. We formulate a thermodynamic topological population mechanics model in which load-bearing entanglements are represented by active and released population densities resolved over orientation, strand stretch and a topological slip-load coordinate. A Helmholtz free energy containing stretch storage, slip-load storage and population entropy defines the active and released chemical potentials. The population exchange is written as a local detailed-balance gain–loss law, so that the reaction contribution to entropy production is non-negative by construction.A conservative finite-volume scheme in orientation space includes mass and positivity checks. Three startup-shear rates identify the exchange/slip pair, a normalized extensional history identifies the stretch-relaxation time, and four shear rates are withheld. The full model gives a held-out shear RMSE of 0.059 versus 0.318 for an independently reidentified no-ξ control with the same number of calibrated quantities, and transfers without refitting to two related solutions using reported relaxation times. The resolved state distinguishes shear-induced topological escape from extensional lock-up and supplies fields of stored stretch and slip-load energy to a notched finite-element model. These results demonstrate a macroscopic contribution of the slip-load coordinate within the tested model. The damage-field calculation assesses sensitivity to the transferred energies and is not presented as material-specific crack-growth validation. © 2026 Elsevier Ltd. All rights are reserved, including those for text and data mining, AI training, and similar technologies.

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