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Heuristic Homogenization of Euler and Pantographic Beams

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.
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Submitted on : Friday, February 7, 2020 - 11:07:47 AM
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Luca Placidi, Francesco Dell'isola, Emilio Barchiesi. Heuristic Homogenization of Euler and Pantographic Beams. Mechanics of Fibrous Materials and Applications, 2020, pp.123-155. ⟨hal-02470313⟩

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