Analytical, numerical and experimental study of the transverse shear behavior of a 3D reinforced sandwich structure

Abstract

Abstract Sandwich structures are known to be very sensitive to transverse shear effects when submitted to out-of-plane loads. The use of a Mindlin–Reissner type equivalent plate model is then certainly the simplest way to take into account these transverse shear strains that strongly influence the global deflection in simple bending. Such a model requires the estimation of the transverse shear stiffness or of the so-called shear correction factor. In the case of a traditional sandwich (with homogeneous foam core), this shear correction factor is set to unity, so that the equivalent transverse shear modulus coincides with the shear modulus of the foam core, which is fatally insubstantial. In order to improve the through-thickness properties of sandwiches, which are governed by the core layer, use is made of thin-walled core materials or reinforcements. In these more complicated cases, the equivalent shear modulus of the core material (in a 3D framework) highly depends on the geometry of the reinforcements and may only be calculated numerically. Moreover, the use of this homogenized shear modulus for the heterogeneous core layer and of a shear correction factor of unity does not generally convey to the proper value of the transverse shear stiffness, due to the possible interactions between the reinforcements and the skins. This paper particularly deals with sandwich structures manufactured with polymeric foam core reinforced thanks to the Napco ® technology (which is based on transverse needle punching) and is devoted to obtaining their transverse shear stiffness. Bearing in mind the remarks made earlier, a one-step homogenization procedure is employed, involving simultaneously the contribution of the reinforcements to the equivalent shear modulus of the reinforced foam core and the interactions between reinforcements and skins. An analytical (respectively numerical) solution is derived, considering a 2D (respectively 3D) unit cell and using the basic principle of energy equivalence. The transverse shear stiffnesses obtained by these two simplified methods are then compared to the one obtained by a finite element numerical computation on a whole beam-like structure for validation purposes, and finally confronted to the experimental values resulting from 3-point bending tests performed with various volume fractions of reinforcements.