A complete description of bi-dimensional anisotropic strain-gradient elasticity

Nicolas Auffray (1) , Justin Dirrenberger (2) , G Rosi (1)

1 MSME - Laboratoire de Modélisation et Simulation Multi Echelle
2 PIMM - Laboratoire Procédés et Ingénierie en Mécanique et Matériaux

In the present paper spaces of fifth-order tensors involved in bidimensional strain gradient elasticity are studied. As a result complete sets of matrices representing these tensors in each one of their anisotropic system are provided. This paper completes and ends some previous studies on the subject providing a complete description of the anisotropic bidimensional strain gradient elasticity. It is proved that this behavior is divided into 14 non equivalent anisotropic classes, 8 of them being isotropic for classical elasticity. The classification and matrix representations of the acoustical gyrotropic tensor are also provided, these results may find interesting applications to the study of waves propagation in dispersive micro-structured-media.

Mots clés: Acoustical activity; Strain gradient elasticity; Chirality; Higher-order tensors; Anisotropy

Domaines: Mécanique des solides [physics.class-ph]; Science des matériaux [cond-mat.mtrl-sci]

Nicolas Auffray, Justin Dirrenberger, G Rosi. A complete description of bi-dimensional anisotropic strain-gradient elasticity. International Journal of Solids and Structures, 2015, 69–70, pp.195-206. ⟨10.1016/j.ijsolstr.2015.04.036⟩. ⟨hal-01145736⟩