This paper proposes a constitutive law and a method for characterizing highly preloaded viscoelastic materials subjected to linear (small-amplitude) vibrations. A multiplicative non-separable variables law has been suggested to model the behavior that depends on both stretch and time/frequency. This approach allows splitting the intricate combined test performed simultaneously on both stretch and frequency

generally in a limited experimental domain up to 100 Hz

into two independent tests. Thus

on one hand

the dynamic complex modulus dependent on frequency alone is evaluated on the basis of vibration tests in a large experimental domain up to 100 kHz. On the other hand

energetic parameters are determined from a quasi-static hyperelastic tensile test. The complex modulus

dependent on both stretch and frequency

is then deduced from the results acquired from uncoupled investigations. This work shows that

in extension

the elastic modulus increases with increasing stretch

and the loss factor decreases with increasing stretch; while

in compression

around the material undeformed state

the modulus increases as the stretch increases till a certain value of compression stretch (upturn point depending on material characteristics)

and then the modulus decreases as the stretch increases. Globally

preload rigidifies materials but reduces their damping property. These results closely match a well-known observation in solid mechanics.