Academic Journal
A third-gradient 1D continuum obtained via asymptotic expansion from a micro-structure obtained constraining a sequence of modified Hart’s antiparallelograms
| Τίτλος: | A third-gradient 1D continuum obtained via asymptotic expansion from a micro-structure obtained constraining a sequence of modified Hart’s antiparallelograms |
|---|---|
| Συγγραφείς: | Rizzi, Nicola, L, Seppecher, Pierre, Dell'Isola, Francesco |
| Συνεισφορές: | Dipartimento di Architettura Roma, Università degli Studi Roma Tre = Roma Tre University (ROMA TRE), Institut de Mathématiques de Toulon - EA 2134 (IMATH), Université de Toulon (UTLN), Università degli Studi dell'Aquila = University of L'Aquila = Université de L'Aquila (UNIVAQ) |
| Πηγή: | ISSN: 1081-2865 ; Mathematics and Mechanics of Solids ; https://hal.science/hal-05459683 ; Mathematics and Mechanics of Solids, 2026, 22 p. ⟨10.1177/10812865251386767⟩. |
| Στοιχεία εκδότη: | CCSD SAGE Publications |
| Έτος έκδοσης: | 2026 |
| Συλλογή: | Université de Toulon: HAL |
| Θεματικοί όροι: | geometrically nonlinear systems, system of trusses, metamaterials, higher gradient continuum models Quannu␣'e␣sciabbole␣stann'a, Third-gradient beam, Third-gradient beam geometrically nonlinear systems system of trusses metamaterials higher gradient continuum models Quannu␣'e␣sciabbole␣stann'a, [PHYS]Physics [physics] |
| Περιγραφή: | International audience ; In this paper, we show one solution of the following synthesis problem: to find a planar, periodic, structure made up of straight bars linked by (perfect) hinges, which, once homogenized, can be modelled as a planar third-gradient one-dimensional (1D) continuum. One possible-solution structure is obtained by considering a suitably Modified Hart’s Antiparallelograms Mechanism (MHAM). Such a mechanism has been conceived in order to get, once suitable kinematical constraints are added, what we call an MHAS, i.e., a Modified Hart’s Antiparallelograms Structure. Each of these structures has a stress-free configuration, i.e., a configuration having vanishing deformation energy, which coincides with a circumference. By limiting to the case when all the mechanism bars are rigid and by replacing specific MHAM elements with two bars interconnected by elastic rotational joints, we get a truss structure which, once homogenized into an elastic 1 D continuum, can assume deformed shapes whose deformation energy is not vanishing only when its curvature is not constant. Choosing for the homogenized 1 D continuum, as a deformation measure, the derivative of curvature, and imposing a suitable rescaling of the rotational elastic moduli, we establish the asymptotic micro-macro relationship for its macro-deformation energy. |
| Τύπος εγγράφου: | article in journal/newspaper |
| Γλώσσα: | English |
| DOI: | 10.1177/10812865251386767 |
| Διαθεσιμότητα: | https://hal.science/hal-05459683 https://hal.science/hal-05459683v1/document https://hal.science/hal-05459683v1/file/rizzi_seppecher_dellisola.pdf https://doi.org/10.1177/10812865251386767 |
| Rights: | https://about.hal.science/hal-authorisation-v1/ ; info:eu-repo/semantics/OpenAccess |
| Αριθμός Καταχώρησης: | edsbas.4DD183E3 |
| Βάση Δεδομένων: | BASE |
| FullText | Text: Availability: 0 CustomLinks: – Url: https://hal.science/hal-05459683# Name: EDS - BASE (ns324271) Category: fullText Text: View record from BASE |
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| Items | – Name: Title Label: Title Group: Ti Data: A third-gradient 1D continuum obtained via asymptotic expansion from a micro-structure obtained constraining a sequence of modified Hart’s antiparallelograms – Name: Author Label: Authors Group: Au Data: <searchLink fieldCode="AR" term="%22Rizzi%2C+Nicola%2C+L%22">Rizzi, Nicola, L</searchLink><br /><searchLink fieldCode="AR" term="%22Seppecher%2C+Pierre%22">Seppecher, Pierre</searchLink><br /><searchLink fieldCode="AR" term="%22Dell'Isola%2C+Francesco%22">Dell'Isola, Francesco</searchLink> – Name: Author Label: Contributors Group: Au Data: Dipartimento di Architettura Roma<br />Università degli Studi Roma Tre = Roma Tre University (ROMA TRE)<br />Institut de Mathématiques de Toulon - EA 2134 (IMATH)<br />Université de Toulon (UTLN)<br />Università degli Studi dell'Aquila = University of L'Aquila = Université de L'Aquila (UNIVAQ) – Name: TitleSource Label: Source Group: Src Data: <i>ISSN: 1081-2865 ; Mathematics and Mechanics of Solids ; https://hal.science/hal-05459683 ; Mathematics and Mechanics of Solids, 2026, 22 p. ⟨10.1177/10812865251386767⟩</i>. – Name: Publisher Label: Publisher Information Group: PubInfo Data: CCSD<br />SAGE Publications – Name: DatePubCY Label: Publication Year Group: Date Data: 2026 – Name: Subset Label: Collection Group: HoldingsInfo Data: Université de Toulon: HAL – Name: Subject Label: Subject Terms Group: Su Data: <searchLink fieldCode="DE" term="%22geometrically+nonlinear+systems%22">geometrically nonlinear systems</searchLink><br /><searchLink fieldCode="DE" term="%22system+of+trusses%22">system of trusses</searchLink><br /><searchLink fieldCode="DE" term="%22metamaterials%22">metamaterials</searchLink><br /><searchLink fieldCode="DE" term="%22higher+gradient+continuum+models+Quannu␣'e␣sciabbole␣stann'a%22">higher gradient continuum models Quannu␣'e␣sciabbole␣stann'a</searchLink><br /><searchLink fieldCode="DE" term="%22Third-gradient+beam%22">Third-gradient beam</searchLink><br /><searchLink fieldCode="DE" term="%22Third-gradient+beam+geometrically+nonlinear+systems+system+of+trusses+metamaterials+higher+gradient+continuum+models+Quannu␣'e␣sciabbole␣stann'a%22">Third-gradient beam geometrically nonlinear systems system of trusses metamaterials higher gradient continuum models Quannu␣'e␣sciabbole␣stann'a</searchLink><br /><searchLink fieldCode="DE" term="%22[PHYS]Physics+[physics]%22">[PHYS]Physics [physics]</searchLink> – Name: Abstract Label: Description Group: Ab Data: International audience ; In this paper, we show one solution of the following synthesis problem: to find a planar, periodic, structure made up of straight bars linked by (perfect) hinges, which, once homogenized, can be modelled as a planar third-gradient one-dimensional (1D) continuum. One possible-solution structure is obtained by considering a suitably Modified Hart’s Antiparallelograms Mechanism (MHAM). Such a mechanism has been conceived in order to get, once suitable kinematical constraints are added, what we call an MHAS, i.e., a Modified Hart’s Antiparallelograms Structure. Each of these structures has a stress-free configuration, i.e., a configuration having vanishing deformation energy, which coincides with a circumference. By limiting to the case when all the mechanism bars are rigid and by replacing specific MHAM elements with two bars interconnected by elastic rotational joints, we get a truss structure which, once homogenized into an elastic 1 D continuum, can assume deformed shapes whose deformation energy is not vanishing only when its curvature is not constant. Choosing for the homogenized 1 D continuum, as a deformation measure, the derivative of curvature, and imposing a suitable rescaling of the rotational elastic moduli, we establish the asymptotic micro-macro relationship for its macro-deformation energy. – Name: TypeDocument Label: Document Type Group: TypDoc Data: article in journal/newspaper – Name: Language Label: Language Group: Lang Data: English – Name: DOI Label: DOI Group: ID Data: 10.1177/10812865251386767 – Name: URL Label: Availability Group: URL Data: https://hal.science/hal-05459683<br />https://hal.science/hal-05459683v1/document<br />https://hal.science/hal-05459683v1/file/rizzi_seppecher_dellisola.pdf<br />https://doi.org/10.1177/10812865251386767 – Name: Copyright Label: Rights Group: Cpyrght Data: https://about.hal.science/hal-authorisation-v1/ ; info:eu-repo/semantics/OpenAccess – Name: AN Label: Accession Number Group: ID Data: edsbas.4DD183E3 |
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| RecordInfo | BibRecord: BibEntity: Identifiers: – Type: doi Value: 10.1177/10812865251386767 Languages: – Text: English Subjects: – SubjectFull: geometrically nonlinear systems Type: general – SubjectFull: system of trusses Type: general – SubjectFull: metamaterials Type: general – SubjectFull: higher gradient continuum models Quannu␣'e␣sciabbole␣stann'a Type: general – SubjectFull: Third-gradient beam Type: general – SubjectFull: Third-gradient beam geometrically nonlinear systems system of trusses metamaterials higher gradient continuum models Quannu␣'e␣sciabbole␣stann'a Type: general – SubjectFull: [PHYS]Physics [physics] Type: general Titles: – TitleFull: A third-gradient 1D continuum obtained via asymptotic expansion from a micro-structure obtained constraining a sequence of modified Hart’s antiparallelograms Type: main BibRelationships: HasContributorRelationships: – PersonEntity: Name: NameFull: Rizzi, Nicola, L – PersonEntity: Name: NameFull: Seppecher, Pierre – PersonEntity: Name: NameFull: Dell'Isola, Francesco – PersonEntity: Name: NameFull: Dipartimento di Architettura Roma – PersonEntity: Name: NameFull: Università degli Studi Roma Tre = Roma Tre University (ROMA TRE) – PersonEntity: Name: NameFull: Institut de Mathématiques de Toulon - EA 2134 (IMATH) – PersonEntity: Name: NameFull: Université de Toulon (UTLN) – PersonEntity: Name: NameFull: Università degli Studi dell'Aquila = University of L'Aquila = Université de L'Aquila (UNIVAQ) IsPartOfRelationships: – BibEntity: Dates: – D: 01 M: 01 Type: published Y: 2026 Identifiers: – Type: issn-locals Value: edsbas – Type: issn-locals Value: edsbas.oa Titles: – TitleFull: ISSN: 1081-2865 ; Mathematics and Mechanics of Solids ; https://hal.science/hal-05459683 ; Mathematics and Mechanics of Solids, 2026, 22 p. ⟨10.1177/10812865251386767⟩ Type: main |
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