Generalized Constraint-Controlled Rheological Model: Two Constitutive Pathways under Sinusoidal Periodic Shear Deformation
Abstract
We formulate the Generalized Constraint-Controlled Rheological Model (GCCRM) for entangled linear and long-arm-branched polymer melts under sinusoidal periodic shear deformation (SPSD), spanning the linear and strongly nonlinear regimes. Molecular architecture, conformation, chain stretch, flow-active constraints, convective constraint release, dynamic tube dilation, and activated arm retraction define a common upstream molecular state. This state feeds two time-domain constitutive pathways (a configurational stress and a dissipative internal-variable stress) which are recombined before Fourier analysis. For branched polymers, the architecture is described by an entire backbone of molecular weight Mbb and Na long arms of molecular weight Ma, with a compliance-weighted representative-constitutive-cell partition. The linear limit is normalized so that the configurational moduli sum to the entanglement modulus, while dynamic tube dilation and stretch drive distinct contributions to dissipative activation. Under reduced closures, GCCRM generates a smooth nonlinear elastic response with an onset of nonlinearity, an approximately logarithmic growth regime, an architecture-dependent maximum, and distinct high-deformation asymptotes. Fourier harmonics, ELR, VLR, and Lissajous curves are treated as post-processing observables of the total stress. The framework establishes a consistent constitutive architecture whose quantitative validation requires one parameter set per material across SPSD and, prospectively, transient shear histories.
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BibTeX
@misc{nichetti2026generalized,
title = {{Generalized Constraint-Controlled Rheological Model: Two Constitutive Pathways under Sinusoidal Periodic Shear Deformation}},
author = {Dario Nichetti and Alessio Zaccone},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.15538},
eprint = {2610.15538},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.15538},
}
RIS
TY - UNPB
TI - Generalized Constraint-Controlled Rheological Model: Two Constitutive Pathways under Sinusoidal Periodic Shear Deformation
AU - Dario Nichetti
AU - Alessio Zaccone
PY - 2026
DA - 2026/10/11
PB - arXiv
DO - 10.48550/arxiv.2610.15538
UR - https://arxiv.org/abs/2610.15538
AB - We formulate the Generalized Constraint-Controlled Rheological Model (GCCRM) for entangled linear and long-arm-branched polymer melts under sinusoidal periodic shear deformation (SPSD), spanning the linear and strongly nonlinear regimes. Molecular architecture, conformation, chain stretch, flow-active constraints, convective constraint release, dynamic tube dilation, and activated arm retraction define a common upstream molecular state. This state feeds two time-domain constitutive pathways (a configurational stress and a dissipative internal-variable stress) which are recombined before Fourier analysis. For branched polymers, the architecture is described by an entire backbone of molecular weight M_bb and N_a long arms of molecular weight M_a, with a compliance-weighted representative-constitutive-cell partition. The linear limit is normalized so that the configurational moduli sum to the entanglement modulus, while dynamic tube dilation and stretch drive distinct contributions to dissipative activation. Under reduced closures, GCCRM generates a smooth nonlinear elastic response with an onset of nonlinearity, an approximately logarithmic growth regime, an architecture-dependent maximum, and distinct high-deformation asymptotes. Fourier harmonics, ELR, VLR, and Lissajous curves are treated as post-processing observables of the total stress. The framework establishes a consistent constitutive architecture whose quantitative validation requires one parameter set per material across SPSD and, prospectively, transient shear histories.
ER -