Fractional viscoelasticity in fractal and non-fractal media: Theory, experimental validation, and uncertainty analysis
| Autor: | Paul Miles, William S. Oates, Somayeh Mashayekhi, M. Yousuff Hussaini |
|---|---|
| Rok vydání: | 2018 |
| Předmět: |
Deformation (mechanics)
Estimation theory Mechanical Engineering Mathematical analysis 02 engineering and technology 021001 nanoscience & nanotechnology Condensed Matter Physics Viscoelasticity 020303 mechanical engineering & transports Fractal 0203 mechanical engineering Orders of magnitude (time) Mechanics of Materials Time derivative Statistical physics Uncertainty quantification 0210 nano-technology Uncertainty analysis Mathematics |
| Zdroj: | Journal of the Mechanics and Physics of Solids. 111:134-156 |
| ISSN: | 0022-5096 |
| DOI: | 10.1016/j.jmps.2017.10.013 |
| Popis: | In this paper, fractional and non-fractional viscoelastic models for elastomeric materials are derived and analyzed in comparison to experimental results. The viscoelastic models are derived by expanding thermodynamic balance equations for both fractal and non-fractal media. The order of the fractional time derivative is shown to strongly affect the accuracy of the viscoelastic constitutive predictions. Model validation uses experimental data describing viscoelasticity of the dielectric elastomer Very High Bond (VHB) 4910. Since these materials are known for their broad applications in smart structures, it is important to characterize and accurately predict their behavior across a large range of time scales. Whereas integer order viscoelastic models can yield reasonable agreement with data, the model parameters often lack robustness in prediction at different deformation rates. Alternatively, fractional order models of viscoelasticity provide an alternative framework to more accurately quantify complex rate-dependent behavior. Prior research that has considered fractional order viscoelasticity lacks experimental validation and contains limited links between viscoelastic theory and fractional order derivatives. To address these issues, we use fractional order operators to experimentally validate fractional and non-fractional viscoelastic models in elastomeric solids using Bayesian uncertainty quantification. The fractional order model is found to be advantageous as predictions are significantly more accurate than integer order viscoelastic models for deformation rates spanning four orders of magnitude. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
|
Full Text from ScienceDirect