Decomposition of the deformations of a thin shell. Nonlinear elastic models

Dominique Blanchard (1) , Georges Griso (2)

1 LMRS - Laboratoire de Mathématiques Raphaël Salem
2 LJLL - Laboratoire Jacques-Louis Lions

We investigate the behavior of the deformations of a thin shell, whose thickness $\delta$ tends to zero, through a decomposition technique of these deformations. The terms of the decomposition of a deformation $v$ are estimated in terms of the $L^2$-norm of the distance from $\nabla v$ to $SO(3)$. This permits in particular to derive accurate nonlinear Korn's inequalities for shells (or plates). Then we use this decomposition technique and estimates to justify a nonlinear bending model for elastic shells for an elastic energy of order $\delta^3$.

Mots clés: shells; Korn's inequality; nonlinear elasticity; gamma-convergence

Domaines: Equations aux dérivées partielles [math.AP]

Dominique Blanchard, Georges Griso. Decomposition of the deformations of a thin shell. Nonlinear elastic models. 2008. ⟨hal-00373296⟩