### Abstract

Lingua originale | English |
---|---|

pagine (da-a) | 014003-014010 |

Numero di pagine | 7 |

Rivista | Physica Scripta |

Volume | TI36 |

Stato di pubblicazione | Published - 2009 |

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### All Science Journal Classification (ASJC) codes

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

### Cita questo

*Physica Scripta*,

*TI36*, 014003-014010.

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

Risultato della ricerca: Article

*Physica Scripta*, vol. TI36, pagg. 014003-014010.

}

TY - JOUR

T1 - Fractional calculus in solid mechanics: local versus non-local approach

AU - Di Paola, Mario

AU - Zingales, Massimiliano

AU - Cornetti, Pietro

AU - Carpinteri, Alberto

AU - Sapora, Alberto

PY - 2009

Y1 - 2009

N2 - Several enriched continuum mechanics theories have been proposed by the scientific community in order to develop models capable of describing microstructural effects. The aim of the present paper is to revisit and compare two of these models, whose common denominator is the use of fractional calculus operators. The former was proposed to investigate damage in materials exhibiting a fractal-like microstructure. It makes use of the local fractional derivative, which turns out to be a powerful tool to describe irregular patterns such as strain localization in heterogeneous materials. On the other hand, the latter is a non-local approach that models long-range interactions between particles by means of the Marchaud fractional derivative. Analogies and differences between the two models are outlined and discussed.

AB - Several enriched continuum mechanics theories have been proposed by the scientific community in order to develop models capable of describing microstructural effects. The aim of the present paper is to revisit and compare two of these models, whose common denominator is the use of fractional calculus operators. The former was proposed to investigate damage in materials exhibiting a fractal-like microstructure. It makes use of the local fractional derivative, which turns out to be a powerful tool to describe irregular patterns such as strain localization in heterogeneous materials. On the other hand, the latter is a non-local approach that models long-range interactions between particles by means of the Marchaud fractional derivative. Analogies and differences between the two models are outlined and discussed.

KW - Fractional Calculus, Fractals, Local Fractional Calculus

UR - http://hdl.handle.net/10447/42333

M3 - Article

VL - TI36

SP - 14003

EP - 14010

JO - Physica Scripta

JF - Physica Scripta

SN - 0031-8949

ER -