On the algebraical structure of isotropic generalized elasticity theories

Nicolas Auffray (1)

1 MSME - Laboratoire de Modélisation et Simulation Multi Echelle

In this paper the algebraical structure of the isotropic nth-order gradient elasticity is investigated. In the classical isotropic elasticity it is well-known that the constitutive relation can be broken down into two uncoupled relations between elementary part of the strain and the stress tensors (deviatoric and spherical). In this paper we demonstrate that this result can not be generalized and since 2nd-order isotropic elasticity there exist couplings between elementary parts of higher-order strain and stress tensors. Therefore, and in certain way, nth-order isotropic elasticity have the same kind of algebraical structure as anisotropic classical elasticity. This structure is investigated in the case of 2nd-order isotropic elasticity, and moduli characterizing the behavior are provided.

Domaines: Mécanique [physics]; Mécanique des solides [physics.class-ph]

Nicolas Auffray. On the algebraical structure of isotropic generalized elasticity theories. Mathematics and Mechanics of Solids, 2015, 20 (5), pp.565-581. ⟨10.1177/1081286513507941⟩. ⟨hal-00856486⟩