Effects of nanoparticle impregnation of polyurethane foam core on the performance of sandwich beams

Polyurethane foam core has been considered for sandwich design due to its high stiffness and toughness. One of the methods of potential improvement of the foam is impregnating it with stiff nanoparticles, increasing its stiffness and collapse strength. In this paper we use the Mori–Tanaka and the self-consistent methods to estimate an increase in the stiffness of closed-cell and open-cell foams impregnated by stiff nanoparticles that do not affect foam geometry. Subsequently, the effect of the impregnation of the foam core on the response of a sandwich beam is demonstrated. The response characteristics considered in the paper include bending deflections in a three-point test, global buckling and wrinkling loads, and the effect of the foam impregnation on its compressive collapse stress associated with local instability of the elements of the foam. Recognizing that the introduction of nanoparticles in the foam material creates local stress concentrations around the inclusions we also examine the local strength of the impregnated foam using the classical Goodier solution for dilute particles and the Mori–Tanaka based stress analysis for a finite particle concentration. In addition, we demonstrate the approach to the evaluation of the resilience of impregnated foam utilizing the dilute approach. While numerical examples concentrate on polyurethane foam, the methodologies and conclusions can be extrapolated to any polymeric foam material reinforced by nanoparticles.