Matrix representations for 3D strain-gradient elasticity

Nicolas Auffray (1) , Hung Le Quang (1) , Qi-Chang He (1)

1 MSME - Laboratoire de Modélisation et Simulation Multi Echelle

The theory of first strain gradient elasticity (SGE) is widely used to model size and non-local effects observed in materials and structures. For a material whose microstructure is centrosymmetric, SGE is characterized by a sixth-order elastic tensor in addition to the classical fourth-order elastic tensor. Even though the matrix form of the sixth-order elastic tensor is well-known in the isotropic case, its complete matrix representations seem to remain unavailable in the anisotropic cases. In the present paper, the explicit matrix representations of the sixth-order elastic tensor are derived and given for all the 3D anisotropic cases in a compact and well-structured way. These matrix representations are necessary to the development and application of SGE for anisotropic materials

Mots clés: Strain gradient elasticity; Anisotropy; Higher order tensors

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

Nicolas Auffray, Hung Le Quang, Qi-Chang He. Matrix representations for 3D strain-gradient elasticity. Journal of the Mechanics and Physics of Solids, 2013, 61 (5), pp.1202-1223. ⟨10.1016/j.jmps.2013.01.003⟩. ⟨hal-00771223⟩