A UNIFIED APPROACH FOR AMPLITUDE DEPENDENT FINITE VISCOELASTICITY OF RUBBER-LIKE MATERIALS

Date

2026-1-19

Author

YILMAZ, Ali Serhat

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Elastomeric materials are extensively used in engineering applications requiring large deformations, such as shock and vibration isolators. The dynamic performance of these components relies heavily on the material's viscoelastic properties, which exhibit complex dependencies on strain amplitude (Payne effect) and loading rate. While numerous models exist to characterize either large-strain viscoelasticity or small-strain dynamic responses individually, a unified framework capable of capturing both phenomena simultaneously remains a significant challenge. In this thesis, a unifying constitutive modeling framework is developed to predict the non-linear rate and amplitude-dependent behavior of filled elastomers. The free energy function is decoupled into equilibrium and non-equilibrium parts. The equilibrium response is characterized by the extended eight-chain model, which accounts for entropic elasticity and topological tube constraints. The non-equilibrium response is formulated using a microsphere-based approach, augmented by a novel non-linear power-law evolution equation and an amplitude-dependent internal variable formulation. This specific structure allows for the prediction of non-linear viscous flow and softening phenomena under varying loading conditions. To validate the model, uniaxial and equibiaxial tension, stress relaxation, and dynamic mechanical analysis (DMA) tests are used. A hierarchical material parameter identification strategy was developed in MATLAB, combining genetic algorithms and gradient-based solvers (\textit{fmincon}). A novel iterative optimization scheme was introduced to overcome the issues for stress superposition. The results demonstrate that the proposed model accurately captures the large-deformation hyperelastic behavior and the time-dependent stress relaxation. Furthermore, the model successfully reproduces the amplitude-dependent softening of the storage modulus associated with the Payne effect. Sensitivity analyses reveal that the proposed power-law exponent critically governs the relaxation behavior, providing a physical basis for tuning the transient response. This unified framework offers a robust tool for the design and analysis of rubber components subjected to complex static and dynamic loading regimes.

Subject Keywords

Finite Viscoelasticity, Payne Effect, Extended Eight-Chain Model, Microsphere Model, Iterative Optimization

URI

https://hdl.handle.net/11511/118751

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Graduate School of Natural and Applied Sciences, Thesis