Relations between loss angles in isotropic linear viscoelastic materials

For the description of the mechanical behaviour of linear viscoelastic materials a number of characteristic material properties is in use. So the relaxation functions in shear, J(t), in extension, D(t), and in compression, B(t), describe the response of the material to a stepfunction H(t) in the corresponding stress. It can be shown theoretically that the relaxation functions are monotonically decreasing functions of time, whereas the retardation functions are monotonically increasing functions of time. It is obvious that Poisson's ratio of a viscoelastic material too is a function of time, so one could define a relaxation Poisson's ratio, c.q. a retardation Poisson's ratio. It cannot be proved, however, that these functions are monotonically decreasing, resp. increasing with time. In case of harmonic deformations a complex Poisson's ratio v* =v' + iv" can be defined. But also here it cannot be proved that complex Poisson's ratio shows either the characteristics of a modulus or of a compliance. The variation of complex Poisson's ratio has been studied theoretically by Gottenberg and Christensen (1) for the special cases where either one or both of G' and G" assume finite non zero values and ~c' or ~c" tend to zero. It turned out that v' is varying between 1 and 0.5, while v" may take positive or negative values. In a similar study Rigbi (2) discussed the special cases where either v" = 0 or ~c"= 0. An experimental study of the complex moduli and Poisson's ratio of several polymers was performed by the present author(3,4), from which it appeared that v' > 0 and v" < 0. Using