Static mechanical response of sandwich panels with bilinear core

A new theoretical model based on the extended high order sandwich panel theory is established to predict the mechanical response of sandwich panels under static loads with the bilinear constitutive stress–strain relation in the core. The constitutive relations of normal stresses related to the longitudinal and vertical normal strains in the bilinear isotropic hardening core are first formulated. The influence of the in-plane rigidity on the elastoplastic response of sandwich structures is analyzed. An in-plane loaded sandwich structure with the bilinear core is first studied based on extended high order sandwich panel theory, and the effect of the bilinear ratio on the mechanical response is evaluated. The governing equations are derived from the principle of minimum potential energy, and a Ritz-based half-analytical method is applied to get the solutions. The plastic response is acquired by an iterative procedure along with the convergence criteria. The results reveal that the local effect can be captured when the axial rigidity of the core is considered. The bilinear characteristic of the core decreases the maximum normal stress with an increase of the average value. The equivalent plastic region extends with the increase of the bilinear ratio when the sandwich structure is loaded in plane. By comparison with open literatures and finite element results, the present theoretical model is proved to be effective and efficient.