Interconversions between linear viscoelastic functions by using relaxation-creep duality representation

Abstract

The interconversions between relaxation moduli and creep compliances, including stretch, shear, bulk parts, and the time-dependent Poisson’s ratio, are derived by using the relaxation-creep duality representation. The relaxation-creep duality representation for the viscoelastic functions introduced in this paper is composed of an exponential function that characterizes the relaxation behavior and a complementary one that characterizes the creep behavior. All viscoelastic functions can be represented as the same form. The new sets of coefficients, called the modulating constants, between viscoelastic functions obey the elastic-like interconversions, and do not involve the characteristic times. The relationships of characteristic times between those functions are also derived. These interconversion formulas can then be calculated easily. Three literatures are referenced to calculate the consistency of the viscoelastic functions via the new interconversions introduced in this work. The Young’s relaxation modulus in one literature is not consistent to the shear one in another literature. By assuming a constant bulk modulus, the modified Young’s relaxation modulus and time-dependent Poisson’s ratio that was derived by the new interconversions can meet the measured curves and can be consistent to the shear creep compliance in the literatures. The fitted data from experiments can then be checked via the new mathematical interconversions for the consistency.