Effective elastic properties of auxetic microstructures : anisotropy and structural applications

Justin Dirrenberger (1) , Samuel Forest (1) , Dominique Jeulin (2)

1 CDM - Centre des Matériaux
2 CMM - Centre de Morphologie Mathématique

Materials presenting a negative Poisson's ratio (auxetics) have drawn attention for the past two decades, especially in the field of lightweight composite structures and cellular media. Studies have shown that auxeticity may result in higher shear modulus, indentation toughness and acoustic damping. In this work, three auxetic periodic microstructures based on 2D geometries are considered for being used as sandwich-core materials. Elastic moduli are computed for each microstructure by using finite elements combined with periodic homogenization technique. Anisotropy of elastic properties is investigated in and out-of-plane. Comparison is made between auxetics and the classical honeycomb cell. A new 3D auxetic lattice is proposed for volumic applications. Cylindrical and spherical elastic indentation tests are simulated in order to conclude on the applicability of such materials to structures. Proof is made that under certain conditions, auxetics can be competitive with honeycomb cells in terms of indentation strength. Their relatively soft response in tension can be compensated, in some situations, by high shear moduli.

Mots clés: Homogenization; Finite element method; Auxetics; Anisotropy; Negative Poisson's ratio; Indentation; Architectured materials; Elasticity

Domaines: Matériaux

Justin Dirrenberger, Samuel Forest, Dominique Jeulin. Effective elastic properties of auxetic microstructures : anisotropy and structural applications. International Journal of Mechanics and Materials in Design, 2013, 9 (1), pp.21-33. ⟨10.1007/s10999-012-9192-8⟩. ⟨hal-00790180⟩