Microscopic Nonaffine Deformation Theory of LAOS in Polymers
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| Formato: | Preprint |
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2026
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| author | Nichetti, Dario Zaccone, Alessio |
| author_facet | Nichetti, Dario Zaccone, Alessio |
| contents | We develop a molecularly motivated framework connecting large-amplitude oscillatory shear (LAOS) nonlinearities in entangled polymers to frequency-dependent nonaffine relaxation in disordered solids. The central idea is that the first harmonic in LAOS measures the residual phase-locked elastic response, whereas the higher harmonics encode the Fourier signature of strain-dependent nonaffine relaxation. The finite-amplitude modulus is interpreted as a local tangent stiffness of the evolving microstructure, in the spirit of elastoplastic and incremental nonaffine models. For entangled polymers, the analogue of the decreasing coordination number in cage-breaking theories of glass mechanics is identified not with the tube-orientation tensor itself, but with the fraction of surviving tube constraints. This distinction leads naturally to a crossover description controlled by a characteristic strain amplitude $γ_c$, rather than by universal fixed power-law exponents. The fitted value $N_{\max}\simeq1.72$ indicates that the present experimental data approach a strong but not fully saturated nonlinear state, remaining below the ideal limiting value predicted for complete constraint collapse. Finally, a constraint-counting argument combining an eight-chain affine network representation with the central-force nonaffine isostatic threshold gives a limiting estimate $|\mathrm{NLI}|_{\max}=3$. The results support the interpretation of the NLI as a Fourier-resolved dynamic nonaffinity parameter and establish a bridge between tube-based polymer dynamics, LAOS harmonic analysis, elastoplastic rheology, and microscopic nonaffine lattice dynamics. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_21021 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Microscopic Nonaffine Deformation Theory of LAOS in Polymers Nichetti, Dario Zaccone, Alessio Soft Condensed Matter Disordered Systems and Neural Networks Statistical Mechanics Chemical Physics We develop a molecularly motivated framework connecting large-amplitude oscillatory shear (LAOS) nonlinearities in entangled polymers to frequency-dependent nonaffine relaxation in disordered solids. The central idea is that the first harmonic in LAOS measures the residual phase-locked elastic response, whereas the higher harmonics encode the Fourier signature of strain-dependent nonaffine relaxation. The finite-amplitude modulus is interpreted as a local tangent stiffness of the evolving microstructure, in the spirit of elastoplastic and incremental nonaffine models. For entangled polymers, the analogue of the decreasing coordination number in cage-breaking theories of glass mechanics is identified not with the tube-orientation tensor itself, but with the fraction of surviving tube constraints. This distinction leads naturally to a crossover description controlled by a characteristic strain amplitude $γ_c$, rather than by universal fixed power-law exponents. The fitted value $N_{\max}\simeq1.72$ indicates that the present experimental data approach a strong but not fully saturated nonlinear state, remaining below the ideal limiting value predicted for complete constraint collapse. Finally, a constraint-counting argument combining an eight-chain affine network representation with the central-force nonaffine isostatic threshold gives a limiting estimate $|\mathrm{NLI}|_{\max}=3$. The results support the interpretation of the NLI as a Fourier-resolved dynamic nonaffinity parameter and establish a bridge between tube-based polymer dynamics, LAOS harmonic analysis, elastoplastic rheology, and microscopic nonaffine lattice dynamics. |
| title | Microscopic Nonaffine Deformation Theory of LAOS in Polymers |
| topic | Soft Condensed Matter Disordered Systems and Neural Networks Statistical Mechanics Chemical Physics |
| url | https://arxiv.org/abs/2605.21021 |