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 |
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| 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 |
| DOI: | 10.1177/10812865251386767 |
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