Nonlinear interaction of geometrical and material properties in sandwich beam instabilities

The first part of this paper is dedicated to the analytical and numerical characterization of local and global sandwich beam instabilities in a perfect linear framework. Analytical loads are extracted from an original unified model and used to understand in depth, through a parametric study, the role played by each geometrical and material parameter in the development of global as well as local instabilities. Also, the effects of the combinations of these characteristics is used to draw precious design indications. A low CPU time-consuming simplified model is then built and assessed. Critical loads and wavelengths computed from this model are shown to correlate very well with analytical predictions. It is established that this first approach is essential in order to lead to more detailed investigations in a numerical nonlinear framework which is the aim of the second part. The first geometrical nonlinear investigations in which linear elastic materials are considered permit to isolate sandwich configurations developing super- or sub-critical post-buckling behaviours. As a general trend, unstable behaviours are rather related to the occurrence of geometrical localizations along the beam. This is illustrated by the drastic effects of the so-called interactive buckling onto the whole stiffness of the sandwich beam. Moreover, it is shown that sandwiches are very sensitive towards imperfection sizes and forms. Eventually, an elastoplastic constitutive law is introduced for the core. It is demonstrated that plastic flow and strain localization in the core, combined with the occurrence of instabilities, are associated with a drastic drop in the global beam stiffness and with a strong decrease of the maximum limit load for some cases. The phenomenon of shear crimping is also observed which can be assimilated to a post-bifurcated development of the global buckling mode.