Fractional calculus in solid mechanics:local versus non-local approach

Mario Di Paola, Massimiliano Zingales, Alberto Carpinteri, Alberto Sapora, Pietro Cornetti

Risultato della ricerca: Article

23 Citazioni (Scopus)

Abstract

Several enriched continuum mechanics theories have been proposed by the scientificcommunity in order to develop models capable of describing microstructural effects. The aimof the present paper is to revisit and compare two of these models, whose commondenominator is the use of fractional calculus operators. The former was proposed toinvestigate damage in materials exhibiting a fractal-like microstructure. It makes use of thelocal fractional derivative, which turns out to be a powerful tool to describe irregular patternssuch as strain localization in heterogeneous materials. On the other hand, the latter is anon-local approach that models long-range interactions between particles by means of the Marchaud fractional derivative. Analogies and differences between the two models areoutlined and discussed.
Lingua originaleEnglish
pagine (da-a)014003-014010
Numero di pagine7
RivistaPhysica Scripta
VolumeTI36
Stato di pubblicazionePublished - 2009

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solid mechanics
Solid Mechanics
Fractional Calculus
calculus
Fractional Derivative
Strain Localization
Heterogeneous Materials
continuum mechanics
Continuum Mechanics
Long-range Interactions
Model
Analogy
Irregular
Microstructure
Fractal
fractals
Damage
damage
operators
microstructure

All Science Journal Classification (ASJC) codes

  • Atomic and Molecular Physics, and Optics
  • Mathematical Physics
  • Condensed Matter Physics

Cita questo

Di Paola, M., Zingales, M., Carpinteri, A., Sapora, A., & Cornetti, P. (2009). Fractional calculus in solid mechanics:local versus non-local approach. Physica Scripta, TI36, 014003-014010.

Fractional calculus in solid mechanics:local versus non-local approach. / Di Paola, Mario; Zingales, Massimiliano; Carpinteri, Alberto; Sapora, Alberto; Cornetti, Pietro.

In: Physica Scripta, Vol. TI36, 2009, pag. 014003-014010.

Risultato della ricerca: Article

Di Paola, M, Zingales, M, Carpinteri, A, Sapora, A & Cornetti, P 2009, 'Fractional calculus in solid mechanics:local versus non-local approach', Physica Scripta, vol. TI36, pagg. 014003-014010.
Di Paola M, Zingales M, Carpinteri A, Sapora A, Cornetti P. Fractional calculus in solid mechanics:local versus non-local approach. Physica Scripta. 2009;TI36:014003-014010.
Di Paola, Mario ; Zingales, Massimiliano ; Carpinteri, Alberto ; Sapora, Alberto ; Cornetti, Pietro. / Fractional calculus in solid mechanics:local versus non-local approach. In: Physica Scripta. 2009 ; Vol. TI36. pagg. 014003-014010.
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AB - Several enriched continuum mechanics theories have been proposed by the scientificcommunity in order to develop models capable of describing microstructural effects. The aimof the present paper is to revisit and compare two of these models, whose commondenominator is the use of fractional calculus operators. The former was proposed toinvestigate damage in materials exhibiting a fractal-like microstructure. It makes use of thelocal fractional derivative, which turns out to be a powerful tool to describe irregular patternssuch as strain localization in heterogeneous materials. On the other hand, the latter is anon-local approach that models long-range interactions between particles by means of the Marchaud fractional derivative. Analogies and differences between the two models areoutlined and discussed.

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