Analytical, numerical and experimental study of the bifurcation and collapse behavior of a 3D reinforced sandwich structure under through-thickness compression

Three-dimensional reinforced sandwich structures are generally designed in order to provide optimal out-of-plane mechanical properties, beside traditional sandwiches which generally display satisfactory specific flexural properties but fatally insubstantial stiffnesses in the through-thickness direction. This paper deals with sandwich structures manufactured with polymeric foam core reinforced thanks to the Napco ® technology (which is based on transverse needling) and specially investigates the compression behavior through the thickness direction. The compressive longitudinal moduli of such sandwiches are shown to be significantly improved in the presence of fibrous orthogonal reinforcements but the experimental estimations rather differ from analytical predictions that can be easily obtained using classical mixture laws. These discrepancies are mainly due to the buckling phenomenon, inherent in the geometry of the reinforcements, and the associated imperfection sensitivity. This work is thus devoted to the prediction of the critical loading of such a sandwich structure under through-thickness compression. A closed-form analytical expression is first derived from a general 3D elastic bifurcation analysis, then compared to finite element numerical solutions (obtained by both linearized buckling and incremental post-buckling analyses) for validation purposes, and finally confronted to experimental results. The buckling phenomenon is actually proved to be mainly responsible for the final collapse of the through-thickness reinforced sandwich.