Séminaire régulier IUSTI – 19 mai 2017 – 11h salle 250

Mechanics of fibrous materials: can Poisson’s function be below 0 or above 1/2?

David Rodney – ILM, Lyon

The mechanics of fibrous materials is both complex and intriguing. Here, we explore one class of such materials, made of the disordered entanglement of a single long coiled fiber. This architected material is of both fundamental and technological interests. From a theoretical point of view, this system can be seen as a disordered material, akin to glasses, but with very long (possibly infinitely) ranged correlations transmitted along the single fiber. From an applied point of view, this material is a potential replacement for sintered materials because of its very large deformability. We study the mechanics of this material using a combination of experiments and simulations. Experimentally, we produced samples from single fibers made of either a superelastic shape-memory alloy, a viscoelastic polymer or a ductile metal. The samples were subjected to deformation cycles, tracking local deformations with optical cameras and x-ray tomography. Numerically, we employed Kirchhoff’s elastic rod theory to simulate the same mechanical cycles on both numerical substitutes of the experimental and on idealized periodic samples. This architecture exhibits surprising mechanical properties, partly because of its topology in-between a discrete and a continuum medium. In particular, we find large and reversible extensions of its volume, both in tension and compression. This material is thus reversibly dilatant in both directions, with a Poisson’s function varying from above 1/2 in compression to less than 0 in tension. This unusual behavior arises from an interplay between the elongation of the coiled wire and rearrangements due to steric effects, which, unlike in traditional discrete media, are reversible when the fiber is elastic. References: – Rodney D., Gadot B., Riu Martinez O., Rolland du Roscoat S., Orgéas L. ‘Reversible dilatancy in entangled single- wire materials’ Nature Materials 15 (2016) 72-77. – Gadot B., Riu Martinez O., Rolland du Roscoat S., Bouvard D., Rodney D., Orgéas L. ‘Entangled single-wire NiTi material: a porous metal with tunable superelastic and shape memory properties’ Acta Materialia 96 (2015) 311-323.