Creep and relaxation tests, performed on various materials like polymers, rubbers and so on are well-fitted by power-laws with exponent β ∈ [0, 1] (Nutting (1921), Di Paola et al. (2011)). The consequence of this observation is that the stress-strain relation of hereditary materials is ruled by fractional operators (Scott Blair (1947), Slonimsky (1961)). A large amount of researches have been performed in the second part of the last century with the aim to connect constitutive fractional relations with some mechanical models by means of fractance trees and ladders (see Podlubny (1999)). Recently, Di Paola and Zingales (2012) proposed a mechanical model that corresponds to fractional stress-strain relation with any real exponent and they have proposed a description of above model (Di Paola et al. (2012)). In this study the authors aim to extend the study to cases with and to fractional Kelvin-Voigt model of hereditariness.

DI PAOLA, M., PINNOLA, F.P., ZINGALES, M. (2012). Fractional differential equations and related exact mechanical models. In Proceedings of the 5° Symposium on Fractional Differentiation and its Applications (pp.1-10). Hohai.

Fractional differential equations and related exact mechanical models

DI PAOLA, Mario;PINNOLA, Francesco Paolo;ZINGALES, Massimiliano
2012-01-01

Abstract

Creep and relaxation tests, performed on various materials like polymers, rubbers and so on are well-fitted by power-laws with exponent β ∈ [0, 1] (Nutting (1921), Di Paola et al. (2011)). The consequence of this observation is that the stress-strain relation of hereditary materials is ruled by fractional operators (Scott Blair (1947), Slonimsky (1961)). A large amount of researches have been performed in the second part of the last century with the aim to connect constitutive fractional relations with some mechanical models by means of fractance trees and ladders (see Podlubny (1999)). Recently, Di Paola and Zingales (2012) proposed a mechanical model that corresponds to fractional stress-strain relation with any real exponent and they have proposed a description of above model (Di Paola et al. (2012)). In this study the authors aim to extend the study to cases with and to fractional Kelvin-Voigt model of hereditariness.
mag-2012
Fractional Differential equations and Applications 2012 (FDA'12)
Hohai
14-17 Maggio
5° Symposium on Fractional Differentiation and its Applications
2012
2012
10
DI PAOLA, M., PINNOLA, F.P., ZINGALES, M. (2012). Fractional differential equations and related exact mechanical models. In Proceedings of the 5° Symposium on Fractional Differentiation and its Applications (pp.1-10). Hohai.
Proceedings (atti dei congressi)
DI PAOLA, M; PINNOLA, FP; ZINGALES, M
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/74526
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