Complex Poisson’s ratio for viscoelastic materials: direct and indirect measurement methods and their correlation

The viscoelastic complex Poisson’s ratio, which describes the frequency-dependent ratio of transverse and longitudinal strains, can be determined directly from simultaneous strain measurements or indirectly from successively measured complex moduli based on the elastic-viscoelastic correspondence principle (EVCP). There has been considerable debate regarding its definition and measurability, with common but often incorrect analogies to complex moduli and compliances. We investigated cylindrical samples of polymethyl methacrylate (PMMA) and Berea sandstone using different measurement set-ups to compare the two methods. For direct measurement, we used strain gauges in harmonic uniaxial tension and compression tests to measure longitudinal and transversal strains. For the indirect method, we measured the complex Young’s and shear moduli by complementing uniaxial tests with torsion experiments on the same specimen under the same conditions using a torsional-axial rheometer. Our analysis on samples from a single product line showed that both methods yielded consistent values for the absolute value of the complex Poisson’s ratio. However, the direct method provided a more accurate determination of its loss factor. Experimental results confirmed that the loss factor of the complex Poisson’s ratio can be positive or negative, depending on which strain lags more behind the axial force excitation, aligning with theoretical expectations.