Identification of the Fractional Zener Model Parameters for a Viscoelastic Material over a Wide Range of Frequencies and Temperatures
Abstract
:1. Introduction
2. Materials and Methods
2.1. Description of the Viscoelastic Material Properties
2.1.1. Hysteresis Loop
2.1.2. Rheological Model of VE Material
2.1.3. Complex Modulus
- for the fractional Kelvin model:
- for the fractional Maxwell model:
2.2. Identification Method
2.2.1. Functional Relationships for the Zener Model
2.2.2. Experimental Data Approximation
2.2.3. Functional Relations for Measured Data
2.2.4. Identification of Model Parameters
2.3. Temperature Influence
3. Results and Discussion
3.1. Test Results for Selected VE Materials
3.1.1. Transverse Shear Test
3.1.2. Longitudinal Shear Test
3.1.3. Construction of a Master Curve Diagram
4. Conclusions
Author Contributions
Funding
Institutional Review Board Statement
Informed Consent Statement
Data Availability Statement
Acknowledgments
Conflicts of Interest
References
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Amplitudes of Approximating Functions | Functional Relationships | ||
---|---|---|---|
[mm] | 0.00556 | 349,503 | |
[mm] | 0.88536 | ||
37.98 | 40,700 | ||
309.21 |
Amplitudes of Approximating Functions | Functional Relationships | ||
---|---|---|---|
0.00116 | [kPa] | 2454.02 | |
0.18445 | |||
[Pa] | 55,551 | [kPa] | 285.78 |
[Pa] | 452,313 |
Model Parameter | Mean Relative Error | |||
---|---|---|---|---|
[%] | [%] | |||
1000 | 18.59 | 16.23 | ||
1400 | 10.75 | 15.37 | ||
1800 | 16.97 | 14.52 | ||
11,600 | 17.45 | 37.99 | ||
16,600 | 10.75 | 15.37 | ||
21,600 | 32.38 | 73.82 | ||
0.014 | 11.65 | 25.64 | ||
0.14 | 10.75 | 15.37 | ||
1.40 | 18.52 | 38.46 | ||
0.22 | 22.36 | 40.97 | ||
0.27 | 10.75 | 15.37 | ||
0.32 | 13.25 | 22.39 |
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Pawlak, Z.M.; Denisiewicz, A. Identification of the Fractional Zener Model Parameters for a Viscoelastic Material over a Wide Range of Frequencies and Temperatures. Materials 2021, 14, 7024. https://doi.org/10.3390/ma14227024
Pawlak ZM, Denisiewicz A. Identification of the Fractional Zener Model Parameters for a Viscoelastic Material over a Wide Range of Frequencies and Temperatures. Materials. 2021; 14(22):7024. https://doi.org/10.3390/ma14227024
Chicago/Turabian StylePawlak, Zdzisław M., and Arkadiusz Denisiewicz. 2021. "Identification of the Fractional Zener Model Parameters for a Viscoelastic Material over a Wide Range of Frequencies and Temperatures" Materials 14, no. 22: 7024. https://doi.org/10.3390/ma14227024