An analytical solution for the large deflections of a slender sandwich beam with a metallic foam core under transverse loading by a flat punch

The large deflections of slender ultralight sandwich beams with a metallic foam core are studied under transverse loading by a flat punch, in which interaction of bending and stretching induced by large deflections is considered. Firstly, a unified yield criterion for metallic sandwich structures considering the effect of core strength is proposed, which is valid for metallic sandwich cross-sections with various core strengths and geometries. This can reduce to the yield criterion for a solid monolithic cross-section and the classical yield criterion for sandwich cross-sections with a weak core, respectively. Then, analytical solutions for the large deflections of fully clamped and simply supported metallic foam core sandwich beams are derived under transverse loading by a flat punch, respectively. Comparisons of the present solutions with experimental results are presented and good agreements are found. The effects of the core strength, the size of loading punch and the boundary conditions on the structural response of sandwich beams are discussed in detail. It is shown that the axial stretching induced by large deflections has significant effect on the load-carrying and energy absorption capacities of sandwich structures in the post-yield regime, and the load-carrying and plastic energy absorption capacities of metallic foam core sandwich beams may be underestimated as the core strength is neglected in analysis, especially for the sandwich beams with a strong core.