Bounds on the imaginary part of complex Poisson’s ratio of viscoelastic materials

Abstract

Bounds on the imaginary part of complex Poisson’s ratio of viscoelastic materials The Poisson’s ratio of ideally elastic solids is a real number for either static or dynamic loading, and has bounds, namely its magnitude can be between -1 and ½ in case of homogeneous, isotropic, linear materials. In contrast, the Poisson’s ratio of viscoelastic solids subjected to dynamic loading can be considered as a complex number, referred to as complex Poisson’s ratio (CPR), because of the material damping. It is clear that the real part of CPR has the same bounds as the Poisson’s ratio. The question what are the bounds on the imaginary part of CPR is investigated in this paper for homogeneous, isotropic, linear viscoelastic materials with positive Poisson’s ratio. It is shown that the imaginary part of CPR also has bounds, which depend on the Poisson’s ratio itself and the material damping. Equations are developed to determine the bounds in question as functions of the Poisson’s ratio and shear loss factor provided that the latter is lower than 0.3. It is proved that the imaginary part of CPR cannot be larger than approximately one tenth part of the shear loss factor. Experimental data supporting the theoretical findings are presented.