Classification of (i) materials’ physical properties, such as the periodic table, Ashby charts, and Abbe diagrams; (ii) instruments, and their precision for experiments used at various length scales; and (iii) organisms have helped in advancing science as well as pedagogy. While it is the linear properties that are often organized in various disciplines of science, in this work, we represented the third-order Murnaghan constants \(\{\ell , m, n\}\) that characterize the nonlinear elastic response of materials. As Ashby charts aid in the selection of materials in novel designs, we have adopted the former to represent \(\{\ell , m, n\}\) , which helps in estimating the residual stresses, among others. The graphical representations indicated that the nonlinear constants (i) exhibit a linear proportionality with Young’s modulus and density in numerical terms and (ii) have a linear interdependence leading to the development of empirical bounds. The values of \(\{\ell , m, n\}\) were the lowest for ceramics and the highest for metals, numerically. It was observed that ceramics possess the minimal elastic nonlinear behavior, whereas metals exhibit the maximal. Additionally, the specific degree of nonlinearity as a function of density was systematically determined for all material categories.
