Heuristic Homogenization of Euler and Pantographic Beams

Luca Placidi (1) , Francesco Dell'Isola (2) , Emilio Barchiesi (3)

1 Faculty of Engineering International Telematic University Uninettuno Rome Italy
2 Dipartimento di Ingegneria Strutturale e Geotecnica [Rome]
3 M&MoCS - International Research Centre on Mathematics & Mechanics of Complex Systems

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.

Domaines: Mécanique [physics]

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⟩