Hencky-type discrete model for pantographic structures: numerical comparison with second gradient continuum models

Emilio Turco (1) , Francesco Dell'Isola (2) , Antonio Cazzani (3) , Nicola Luigi Rizzi (4)

1 DADU, Università degli Studi di Sassari, Sassari
2 UNIROMA - Università degli Studi di Roma "La Sapienza" = Sapienza University [Rome]
3 UniCa - Università degli Studi di Cagliari = University of Cagliari
4 ROMA TRE - Università degli Studi Roma Tre = Roma Tre University

Hencky (Über die angenäherte Lösung von Stabilitätsproblemen im Raum mittels der elastischen Gelenkkette. Ph.D. thesis, Engelmann, 1921) proposed a discrete model for elasticae by introducing rigid bars and rotational springs. Hencky (Proc R Soc Lond A Math Phys Eng Sci 472(2185), 2016) approach has been introduced to heuristically motivate the need of second gradient continua. Here, we present a novel numerical code implementing directly the discrete Hencky-type model which is robust enough to solve the problem of the determination of equilibrium configurations in the large deformation and displacement regimes. We apply this model to study some potentially applicable problems, and we compare its performances with those of the second gradient continuum model. The numerical evidence presented supports the conjecture that Hencky-type converges to second gradient model.

Domaines: Mécanique [physics]

Emilio Turco, Francesco Dell'Isola, Antonio Cazzani, Nicola Luigi Rizzi. Hencky-type discrete model for pantographic structures: numerical comparison with second gradient continuum models. Zeitschrift für Angewandte Mathematik und Physik, 2016, 67 (4), pp.85. ⟨10.1007/s00033-016-0681-8⟩. ⟨hal-01345864⟩