A generalized analytical approach to investigate the indentation of sandwich beams under concentrated loads is presented, based on the Winkler foundation theory. A segment-wise model is implemented to the case of fully backed sandwich beams with polymeric foam cores exhibiting generic non-linear compressive behaviours. Closed-form analytical solutions of the indentation curve are obtained for simplified foam compression behaviours: elastic-perfectly-plastic, bilinear and bilinear-perfectly-plastic. Analytical predictions are compared with experimental data from sandwiches employing foam cores with peculiar non-linear behaviours. The proposed models are found to give a better match of the experimental data than the classic elastic-perfectly-plastic model.

Abstract. In this work the indentation behaviour of sandwich beams is studied adopting the classical approach representing the core material as a Winkler-type foundation. It is shown how most of the proposed theories can be derived from a general fourth order linear differential equation expressing the equilibrium of the indented beam skin. Different assumptions on the supporting boundary constraints and materials constitutive behaviour, lead to simplifications of the general equation and to the prediction of different indentation features. An extension of the Segment-Wise approach recently proposed in the literature is in particular presented with potential to better simulate foam cores with markedly non-linear compressive behavior. Results from experimental indentation tests performed on sandwiches employing thermoplastic based matrices and foams are also presented to supplement the theoretical analysis.