Stress gradient elasticity theory : existence and uniqueness of solution

Karam Sab (1, 2) , Frédéric Legoll (2, 3, 1) , Samuel Forest (4)

1 navier umr 8205 - Laboratoire Navier
2 multi-échelle - Modélisation et expérimentation multi-échelle pour les solides hétérogènes
3 MATHERIALS - MATHematics for MatERIALS
4 CDM - Centre des Matériaux

The objective of the present article is to assess the well-posedness of the stress gradient linear elastic problems recently introduced by Forest and Sab (Mech. Res. Commun. 40:16–25, 2012) and to formulate the corresponding existence and uniqueness theorems. In particular, we show that such theorems can be established in the case of the boundary value problems formulated in (Forest and Sab in Mech. Res. Commun. 40:16–25, 2012) with the corresponding boundary conditions.

Mots clés: Stress gradient elasticity; existence and uniqueness of solution; higher order elasticity; boundary conditions

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

Karam Sab, Frédéric Legoll, Samuel Forest. Stress gradient elasticity theory : existence and uniqueness of solution. Journal of Elasticity, 2016, 123 (2), pp.179-201. ⟨10.1007/s10659-015-9554-1⟩. ⟨hal-01288563⟩