A Data-Driven Nonlinear Viscoelasticity Model for Rubbery Polymers

Date

2026-6-19

Author

Durna, Recep

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Rubbery polymers exhibit nonlinear elastic behavior together with time- and rate-dependent viscous effects arising from irreversible energy dissipation mechanisms. Capturing these responses through predefined analytical forms is challenging, as such conventional constitutive frameworks often lack sufficient versatility across diverse material classes. In this work, a thermodynamically consistent, data-driven constitutive framework is proposed for finite viscoelasticity. Previous studies have shown that B-spline-based formulations can effectively represent hyperelastic material behavior. Herein, the spline-based approach is extended to nonlinear viscoelasticity to determine the form of the evolution of internal variables within a multinetwork setting. The equilibrium response is modeled using either an extended eight-chain formulation, when sufficient to represent the data, or a spline-based modified invariant formulation when a more flexible and form-free representation is required. In the latter, control points are selected to satisfy necessary polyconvexity constraints. The nonequilibrium response is addressed through Maxwell-type branches incorporating hyperelastic and dashpot elements. Eight-chain or extended eight-chain formulations are employed for the hyperelastic spring elements, depending on the need for a second invariant term. For the inelastic flow, a form-free B-spline-based formulation is developed that satisfies the second law of thermodynamics and is compatible with finite element implementations. The predictive capability of the proposed framework is demonstrated through validation against experimental datasets for three distinct rubber types. Furthermore, calibrated parameters are utilized to extrapolate secondary datasets, showcasing the framework's robustness. Overall, the proposed framework provides a flexible, physically grounded alternative to classical phenomenological models for describing viscoelastic behavior under finite deformations.

Subject Keywords

Data-driven constitutive modeling, Finite viscoelasticity, Thermodynamic consistency, Polyconvexity, Algorithmic setting

URI

https://hdl.handle.net/11511/119744

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Graduate School of Natural and Applied Sciences, Thesis