CONSTITUTIVE MODELING AND EXPERIMENTAL IDENTIFICATION OF MATERIAL PARAMETERS OF VISCOELASTIC MATERIALS BY VARIABLE ORDER NON-INTEGER DERIVATIVES

Date

2025-3-4

Author

Çakır, Muhammed

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Polymeric materials are widely used due to their ease of manufacture, low density, and cost-effectiveness. Their viscoelastic properties, such as stress relaxation and creep, arise from their long molecular chains. Traditional rheological models describing these properties often require numerous parameters, as they rely on multiple springs and dashpots with estimated constants. An alternative approach is fractional calculus, which employs non-integer derivatives and integrals to simplify the modeling process. This method reduces the number of required parameters while providing a more consistent representation of mechanical behavior by allowing the order of differentiation to vary between 0 and 1—representing purely elastic and purely viscous behavior, respectively. The mechanical properties of viscoelastic materials are strongly influenced by environmental factors and loading/deformation history, necessitating a variable-order fractional model rather than a constant-order one. In this study, fractional-order viscoelastic models are applied to materials such as PE300, PTFE, and EVA, utilizing tensile test data. Theoretical models and MATLAB-based simulations are validated through comparisons with experimental results and finite element analysis (FEA). To further enhance predictive accuracy, user-defined material subroutines are developed for the commercial finite element solver ABAQUS, incorporating both constant-order and variable-order formulations. Further verification of the proposed approach is conducted using the tensile test data obtained from a tensile testing machine equipped with non-contact strain measurement devices. The methodology is assessed by simulating tensile tests providing a comprehensive evaluation of the parameter estimation method. Additionally, the effectiveness of the user material subroutine is examined by comparing simulation results with experimental data, ensuring the reliability of the proposed framework.

Subject Keywords

Viscoelasticity, Fractional Calculus, Variable Order

URI

https://hdl.handle.net/11511/114097

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Graduate School of Natural and Applied Sciences, Thesis