Characterization of complex modulus of viscoelastic materials subject to static compression

In this paper, a procedure to estimate complex modulus of incompressible viscoelastic materials from stiffness measurements as functions of frequency under heavy compressive pre-strain is presented together with some results for a typical viscoelastic material. Two existing methods are discussed which enable predictions of the complex modulus based on the measurements as functions of frequency and pre-strain. A new more efficient formula is proposed which obtains the modulus by combining the frequency effects at a reference pre-strain and the pre-strain effects at a chosen frequency, i.e., dynamic effects. This formula reflects the trend of dynamic modulus with the static compression under the assumption that the relaxation function is dependent on the static compression. The relaxation function can be transformed into frequency-dependent functions, which are modified to represent the pre-strain effect at a chosen frequency. Dynamic properties of a viscoelastic material were obtained at a given strain amplitude from 1 to 180 Hz under nine levels of compressive pre-strain and performances of the formulas are comparatively discussed.