New insights on the applicability of Eringen's nonlocal theory

New insights on the applicability of Eringen's nonlocal theory are introduced. Eringen's nonlocal theory which assumes the same attenuation function for all material moduli is assessed according to its ability to reflect the exact dispersions of different materials. It is revealed that Eringen's nonlocal theory fails to, simultaneously, fit both the longitudinal and transverse (shear) acoustic dispersion curves of some materials, such as Si, Au, and Pt. In order to extend the limits of applicability of Eringen's nonlocal theory, a general form of the nonlocal theory is developed. This general nonlocal theory considers different attenuation functions for the distinct material moduli. This makes the proposed nonlocal theory easily fits both the longitudinal and transverse acoustic dispersion curves of different materials. Moreover, unlike Eringen's conventional form of nonlocal theory, the general nonlocal theory can reflect both hardening and softening behaviors of the material. Another contribution in this study is the determination of the nonlocal parameters for various crystal materials by fitting their dispersions with the proposed nonlocal theory. Thus, the elastic moduli and the nonlocal parameters of metallic crystals (such as Au, Ag, Cu, and Pt), diamond structure crystals (such as diamond and Si), layered structure crystals (such as graphite), Metal Oxides and Alkali Halides with Rock-Salt structures (such as BaO, NiO, LiH and LiD), and Fluorite structure crystals (such as Mg2Sn and Mg2Pb) are reported.