Modeling of a compact functionally graded cellular structure: a finite element study for medium and high strain rates

The work discussed here is a continuation of study performed previously (Ali et al. in Int J Adv Eng Softw 39:95–106, 2008), in which we presented a detailed analysis of quasi-static and low dynamic response (up to strain rates of 1,200 s−1) for a compact functionally graded cellular structure found in a banana peel. In this paper, we focus on the in-plane response of the graded structure under medium and high velocity impacts (strain rates ranging from 2,400 to 12,416 s−1). A theoretical model developed earlier (Ali et al. in Int J Adv Eng Softw 39:95–106, 2008) for predicting the static, quasi-static, and low dynamic response of the graded structure is modified to take into account high dynamic effects. Different critical energy absorbing characteristics, e.g., deformation modes, collapsing mechanism, crushing stress, locking strain, total energy absorbed, etc. are discussed. The output of the high strain analytical model is compared with finite element simulations. The results show that the analytical model aligns well with finite element output for high dynamic cases.