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EnglishThis chapter is devoted to the application of fractional calculus in mechanics of materials and thermodynamics. The use of fractional calculus in mechanics is related to the definition of fractional-order constitutive equations leading to the class of fractional hereditariness. In this regard, a brief description of the classical rheological models of material hereditariness and a comparison with the fractional elements are reported. It is shown that a rheological hierarchy corresponding to the fractional order stress-strain relation may be defined. Such a model provides a multi-scale mechanical picture of the power-law hereditariness and it leads toward an unique definition of material free energy. The chapter is also devoted to the investigation of the fractional-order Fourier equation. The analysis of the anomalous heat transfer has been conducted with the a multi-scale approach similar to that used in material hereditariness. Thermodynamic consistency of the model has been reported in terms of the irreversible entropy production.
Pinnola F.P., & Zingales M. (2019). Fractional-order constitutive equations in mechanics and thermodynamics. In V.E. Tarasov (a cura di), Handbook of Fractional Calculus with Applications: Volume 4: Applications in Physics, Part A (pp. 277-304). De Gruyter.
| Data di pubblicazione: | 2019 | |
| Titolo: | Fractional-order constitutive equations in mechanics and thermodynamics | |
| Autori: | ZINGALES, Massimiliano [Investigation] | |
| Citazione: | Pinnola F.P., & Zingales M. (2019). Fractional-order constitutive equations in mechanics and thermodynamics. In V.E. Tarasov (a cura di), Handbook of Fractional Calculus with Applications: Volume 4: Applications in Physics, Part A (pp. 277-304). De Gruyter. | |
| Abstract: | This chapter is devoted to the application of fractional calculus in mechanics of materials and thermodynamics. The use of fractional calculus in mechanics is related to the definition of fractional-order constitutive equations leading to the class of fractional hereditariness. In this regard, a brief description of the classical rheological models of material hereditariness and a comparison with the fractional elements are reported. It is shown that a rheological hierarchy corresponding to the fractional order stress-strain relation may be defined. Such a model provides a multi-scale mechanical picture of the power-law hereditariness and it leads toward an unique definition of material free energy. The chapter is also devoted to the investigation of the fractional-order Fourier equation. The analysis of the anomalous heat transfer has been conducted with the a multi-scale approach similar to that used in material hereditariness. Thermodynamic consistency of the model has been reported in terms of the irreversible entropy production. | |
| Digital Object Identifier (DOI): | http://dx.doi.org/10.1515/9783110571707-012 | |
| Appare nelle tipologie: | 2.01 Capitolo o Saggio |
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