Exact Mechanical Hierarchy of Non-Linear Fractional-Order Hereditariness
Non-local time evolution of material stress/strain is often referred to as material hereditariness. In this paper, the widely used non-linear approach to single integral time non-local mechanics named quasi-linear approach is proposed in the context of fractional differential calculus. The non-linea...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-04-01
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| Series: | Symmetry |
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| Online Access: | https://www.mdpi.com/2073-8994/12/4/673 |
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| author | Gioacchino Alotta Emanuela Bologna Massimiliano Zingales |
| author_facet | Gioacchino Alotta Emanuela Bologna Massimiliano Zingales |
| author_sort | Gioacchino Alotta |
| collection | DOAJ |
| description | Non-local time evolution of material stress/strain is often referred to as material hereditariness. In this paper, the widely used non-linear approach to single integral time non-local mechanics named quasi-linear approach is proposed in the context of fractional differential calculus. The non-linear model of the springpot is defined in terms of a single integral with separable kernel endowed with a non-linear transform of the state variable that allows for the use of Boltzmann superposition. The model represents a self-similar hierarchy that allows for a time-invariance as the result of the application of the conservation laws at any resolution scale. It is shown that the non-linear springpot possess an equivalent mechanical hierarchy in terms of a functionally-graded elastic column resting on viscous dashpots with power-law decay of the material properties. Some numerical applications are reported to show the capabilities of the proposed model. |
| first_indexed | 2024-03-10T20:16:03Z |
| format | Article |
| id | doaj.art-0b6d7639ceb54fa19a93c92b622bbbab |
| institution | Directory Open Access Journal |
| issn | 2073-8994 |
| language | English |
| last_indexed | 2024-03-10T20:16:03Z |
| publishDate | 2020-04-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Symmetry |
| spelling | doaj.art-0b6d7639ceb54fa19a93c92b622bbbab2023-11-19T22:30:46ZengMDPI AGSymmetry2073-89942020-04-0112467310.3390/sym12040673Exact Mechanical Hierarchy of Non-Linear Fractional-Order HereditarinessGioacchino Alotta0Emanuela Bologna1Massimiliano Zingales2Dipartimento di Ingegneria Civile, dell’Energia, dell’Ambiente e dei Materiali, Università degli Studi “Mediterranea” di Reggio Calabria, 89124 Reggio Calabria, ItalyDipartimento di Ingegneria, Viale delle scienze eq.8, 90128 Palermo, ItalyDipartimento di Ingegneria, Viale delle scienze eq.8, 90128 Palermo, ItalyNon-local time evolution of material stress/strain is often referred to as material hereditariness. In this paper, the widely used non-linear approach to single integral time non-local mechanics named quasi-linear approach is proposed in the context of fractional differential calculus. The non-linear model of the springpot is defined in terms of a single integral with separable kernel endowed with a non-linear transform of the state variable that allows for the use of Boltzmann superposition. The model represents a self-similar hierarchy that allows for a time-invariance as the result of the application of the conservation laws at any resolution scale. It is shown that the non-linear springpot possess an equivalent mechanical hierarchy in terms of a functionally-graded elastic column resting on viscous dashpots with power-law decay of the material properties. Some numerical applications are reported to show the capabilities of the proposed model.https://www.mdpi.com/2073-8994/12/4/673fractional calculusnon-linear springpotmechanical hierarchy |
| spellingShingle | Gioacchino Alotta Emanuela Bologna Massimiliano Zingales Exact Mechanical Hierarchy of Non-Linear Fractional-Order Hereditariness Symmetry fractional calculus non-linear springpot mechanical hierarchy |
| title | Exact Mechanical Hierarchy of Non-Linear Fractional-Order Hereditariness |
| title_full | Exact Mechanical Hierarchy of Non-Linear Fractional-Order Hereditariness |
| title_fullStr | Exact Mechanical Hierarchy of Non-Linear Fractional-Order Hereditariness |
| title_full_unstemmed | Exact Mechanical Hierarchy of Non-Linear Fractional-Order Hereditariness |
| title_short | Exact Mechanical Hierarchy of Non-Linear Fractional-Order Hereditariness |
| title_sort | exact mechanical hierarchy of non linear fractional order hereditariness |
| topic | fractional calculus non-linear springpot mechanical hierarchy |
| url | https://www.mdpi.com/2073-8994/12/4/673 |
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