Interconversions between linear viscoelastic functions with a time-dependent bulk modulus

Abstract

The interconversion relations for viscoelastic functions are derived with the consideration of the time-dependent bulk modulus, K(t), for both traditional and fractional Prony series representations of viscoelasticity. The application of these relations is to replace the fitting parameters of Young’s relaxation modulus, E(t), by the unknown parameters of K(t) and the known parameters of the shear relaxation modulus, G(t), and to fit the E(t) to the experimental data for obtaining the parameters of K(t). The fitting results show that only two experiments for measuring the viscoelastic functions of an isotropic material are not enough to determine the other viscoelastic functions. However, if we consider the relaxation rates of K(t) and G(t), we may conclude that the constant bulk modulus is a more reasonable assumption, and the corresponding Poisson’s ratio, ν(t), is a monotonic-increasing function.

Indirect Identification of the Complex Poisson's Ratio in Fractional Viscoelasticity

“…The methodology proposed in the present paper consists of a grouping of common parameters of the complex Young's and shear moduli and establishing a hybrid optimization process. To this end, according to Ernst et al (2003), Lakes andWinemam (2006), O'Brien et al (2007), and Chen et al (2017), it is considered that the influence of temperature and the differentiation orders are the same for both the complex Young's and shear moduli. In addition, according to Waterman (1977), Tschoegl (1989), and Pritz (1998), the Poisson's ratio of a rubbery material only has only has physical meanings when its real part fluctuates between 0 and 0.5 -and is thus monotonically decreasing-along the frequency.…”

“…On the other hand, according to Ernst et al (2003), Lakes andWinemam (2006), O'Brien et al (2007), and Chen et al (2017), the influence of temperature and the orders of differentiation are the same for both complex moduli (Young's or shear). In this case, the WLF constants can be obtained as…”

“…It is notable that such considerations ignore time and frequency effects. However, in practice, this parameter is variable in frequency, as well as in time (Pritz, 1998;Pritz, 2000;Tschoegl et al, 2002;Pritz, 2007;Chen et al, 2017).…”

“…On the other hand, in indirect methods, the identification occurs by constructing and evaluating auxiliary complex viscoelastic functions (Young's, shear and/or bulk modulus). The present work focuses on the indirect method, which has been little explored by researchers in recent decades (Philippoff and Brodnyan, 1955;Koppelman, 1959;Thomson, 1966;Waterman, 1977;Pritz,1998;Pritz, 2000;Pritz, 2007;Chen et al, 2017).…”

“…In SI, the units of E b and E  are, respectively, s  and MPa . In general, during the identification of VEMs, several works find proper adjustments when Espíndola et al, 2006;Agirre and Elejabarrieta, 2010;Guedes, 2011;Ciniello et al, 2016;Chen et al, 2017;Sousa et al, 2017). , and strains, ( ) t  , in pure shear tests.…”