The main aim of this study is to develop a new approach for analysis of second-order pressure derivative of bulk modulus \(\text B^{\prime\prime}_{0}\) by utilizing the values of first-order pressure derivative of bulk modulus B0 and zero order pressure derivative of bulk modulus B0. The study of \(\text B^{\prime\prime}_{0}\) is useful in analysing second-order pressure derivative of bulk modulus EOS, and it is found after applying Tait EOS and Gupta and Gupta (equation of state) EOS. The novelty of this work lies in the analytical expression presented as equation (5), which enables direct estimation of \(\text B^{\prime\prime}_{0}\) without requiring high-order fitting or complex datasets. The pressure dependent elastic behaviour of nanomaterials also depends on the variation of (V/V0). The obtained data are used in the numerical simulation of the high pressure compression behaviour of nanomaterials, and are compared with the available experimental data and other equations of states. Moreover, nanomaterials viz., carbon nanotube (individual), Fe-filled MWCNT, Zr0.1Ti0.9O2 and α-Fe (filled nanotube) are used to verify this model and the method demonstrates strong agreement with experimental data, confirming its applicability.
