Indentation in lightweight composite sandwich beams

Indentation law is the relationship between force and deflection under the load on a sandwich beam in a fully backed state (on rigid ground), which plays an important role in low-velocity impact models. In the classical method, the Winkler model, which is based on analysing a beam on elastic foundation, is used for measuring the linear part of indentation law and core compression yielding load. This load is assumed to be the same as three-point bending (3PB) state core compression yielding load. In the present article, the sandwich beam is divided into three regions: two faces and a core. Faces are modelled with classical beam theory separately and the core is modelled with two-dimensional elasticity theory, which is known as sandwich panel higher-order theory (SPHOT). A simply supported and fully backed sandwich beam with concentrated loading is solved with Fourier series, and closed-form solutions for core compression, shear, and normal stresses of the core are obtained. The obtained core yielding load by SPHOT is compared with the classical method using the commercial finite element code ANSYS and also with recently reported researches in the literature. The results show that SPHOT predicts more accurate core yielding load and better indentation law compared with other theories and are in good agreement with the results of finite element simulation. In addition, differences between SPHOT theory and the classical method for indentation are investigated in terms of geometry and material properties of sandwich elements. The bottom face effect is determined in core compression in the 3PB state. It is shown that core compression in the 3PB state is lower than fully backed indentation and fully backed indentation is lower than classical prediction.