A critical evaluation of mechanical models for sandwich beams

Abstract

We focus on the description of the stress state of sandwich beams under bending and shear, a non-trivial task if Saint-Venant's principle does not hold, as it is the case if the skins are somewhat stiffer than the core. Each of the analytical structural models available in literature turns out to be accurate for a limited range of relative stiffness between core and skins, or sandwich heterogeneity. For a simply supported sandwich beam subject to uniform transversal load, we evaluate the stress by means of (a) the classical theory relying on the linear cross-section kinematics, appropriate if Saint-Venant's principle holds, (b) the structural theory based on the zig-zag warping (e.g. Krajcinovic D. Sandwich beam analysis. J Appl Mech, Trans ASME 1972; 39(3): 773–778), and (c) the higher-order theory of Frostig et al. (Frostig Y, Baruch M, Vilnay O, et al. High-order theory for sandwich-beam behavior with transversely flexible core. J Eng Mech, Trans ASCE 1992; 118(5): 1026–1043), the latter usually appropriate when the core is much softer than the skins. The results are compared, for several combinations of material and geometrical parameters, with those of finite element simulations in which the sandwich is modelled as a plane stress continuum. This comparison allows us to provide some graphs which can help in selecting the model appropriate for each sandwich heterogeneity. This is accomplished in terms of non-dimensional material and geometrical parameters the sandwich heterogeneity depends on. We identify and discuss two levels of heterogeneity at which one should switch analytical model: one level is related to the validity of Saint-Venant's principle, while the other level is concerned with the definition of antiplane sandwich.