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Article Dans Une Revue European Journal of Mechanics - A/Solids Année : 2009

Bounds for the effective properties of heterogeneous plates

Résumé

This paper presents new bounds for heterogeneous plates which are similar to the well-known Hashin-Shtrikman bounds, but take into account plate boundary conditions. The Hashin-Shtrikman variational principle is used with a self-adjoint Greeen-operator with traction-free boundary conditions proposed by the authors. This variational formulation enables to derive lower and upper bounds for the effective in-plane and out-of-plane elastic properties of the plate. Two applications of the general theory are considered: first, in-plane invariant polarization fields are used to recover the ”first-order” bounds proposed by Kolpakov(1999) for general heterogeneous plates; next, ”second-order bounds” for n-phase plates whose constituents are statistically homogeneous in the in-plane directions are obtained. The results related to a two-phase material made of elastic isotropic materials are shown. The ”second-order” bounds for the plate elastic properties are compared with the plate properties of homogeneous plates made of materials having an elasticity tensor computed from ”second-order” Hashin-Shtrikman bounds in an infinite domain.
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Dates et versions

hal-00509236 , version 1 (11-08-2010)

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Trung-Kien Nguyen, Karam Sab, Guy Bonnet. Bounds for the effective properties of heterogeneous plates. European Journal of Mechanics - A/Solids, 2009, 28 (6), pp.1051-1063. ⟨10.1016/j.euromechsol.2009.05.006⟩. ⟨hal-00509236⟩
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