In the present contribution, we address the following problem: is it possible to find a microstructure producing, at the macro-level and under loads of the same order of magnitude, a beam which can be both extensible and flexible? Using an asymptotic expansion and rescaling suitably the involved stiffnesses, we prove that a pantographic microstructure does induce, at the macro-level, the aforementioned desired mechanical behavior. Thus, in an analogous fashion to that of variational asymptotic methods, and following a mathematical approach resembling that used by Piola, we have employed asymptotic expansions of kinematic descriptors directly into the postulated energy functional and a heuristic homogenization procedure is presented and applied to the cases of Euler and pantographic beams.

Heuristic homogenization of Euler and pantographic beams / Placidi, L.; Dell'Isola, F.; Barchiesi, E.. - 596:(2020), pp. 123-155. [10.1007/978-3-030-23846-9_3]

Heuristic homogenization of Euler and pantographic beams

Barchiesi E.
2020-01-01

Abstract

In the present contribution, we address the following problem: is it possible to find a microstructure producing, at the macro-level and under loads of the same order of magnitude, a beam which can be both extensible and flexible? Using an asymptotic expansion and rescaling suitably the involved stiffnesses, we prove that a pantographic microstructure does induce, at the macro-level, the aforementioned desired mechanical behavior. Thus, in an analogous fashion to that of variational asymptotic methods, and following a mathematical approach resembling that used by Piola, we have employed asymptotic expansions of kinematic descriptors directly into the postulated energy functional and a heuristic homogenization procedure is presented and applied to the cases of Euler and pantographic beams.
2020
978-3-030-23845-2
978-3-030-23846-9
Heuristic homogenization of Euler and pantographic beams / Placidi, L.; Dell'Isola, F.; Barchiesi, E.. - 596:(2020), pp. 123-155. [10.1007/978-3-030-23846-9_3]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11388/280571
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