Apparent negative values of Young's moduli of lattice materials under dynamic conditions

Adhikari, S., Mukhopadhyay, T., Shaw, A. and Lavery, N. P. (2020) Apparent negative values of Young's moduli of lattice materials under dynamic conditions. International Journal of Engineering Science, 150, [103231]. (doi:10.1016/j.ijengsci.2020.103231).

Abstract

Lattice materials are characterised by their equivalent elastic moduli for analysing mechanical properties of the microstructures. The values of the elastic moduli under static forcing condition are primarily dependent on the geometric properties of the constituent unit cell and the mechanical properties of the intrinsic material. Under a static forcing condition, the equivalent elastic moduli (such as Young's modulus) are always positive. When dynamic forcing is considered, the equivalent elastic moduli become functions of the applied frequency and they can be negative at certain frequency values. This paper, for the first time, explicitly demonstrates the occurrence of negative equivalent Young's modulus in lattice materials experimentally. Using additively manufactured titanium-alloy lattice metastructures, it is shown that the real part of experimentally measured in-plane Young's modulus becomes negative under a dynamic environment. In fact, we show that the onset of such negative Young's modulus in lattice materials can be precisely determined by capturing the sub-wavelength scale dynamics of the system. Experimental confirmation of the negative Young's moduli and the onset of the same as a function of frequency provide the necessary physical insights and confidence for its potential exploitation in various multi-functional structural systems and devices across different length scales.

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