Linear elastic trusses leading to continua with exotic mechanical interactions

Pierre Seppecher (1, 2, 3) , Jean-Jacques Alibert (2) , Francesco Dell'Isola (4, 5, 1)

1 M&MoCS - International Research Centre on Mathematics & Mechanics of Complex Systems
2 IMATH - Institut de Mathématiques de Toulon - EA 2134
3 ANLA - Laboratoire d'Analyse Non Linéaire Appliquée
4 Dipartimento di Ingegneria Strutturale e Geotecnica
5 Laboratorio Strutture e Materiali Intelligenti - Fondazione Tullio Levi-Civita

We study the statics of some trusses, i.e. networks of nodes linked by linear springs. The trusses are designed in such a way that a few number of floppy modes are present and remain when considering the homogenized limit of the truss. We then obtain linear elastic materials with exotic mechanical interactions which cannot be described in the classical framework of Cauchy stress theory. For aim of simplicity, the structures described here are two-dimensional. The extension to the 3D case does not present any difficulty.

Domains: Mechanics [physics.med-ph]

Pierre Seppecher, Jean-Jacques Alibert, Francesco Dell'Isola. Linear elastic trusses leading to continua with exotic mechanical interactions. Journal of Physics: Conference Series, 2011, 319 (1), 13 p. ⟨hal-00630098⟩