Characterization of damping properties of nonlinear viscoelastic materials

The dynamic behavior of most polymeric materials become non-linear at a moderately large strain amplitude excitation. In order to optimize their uses for noise and vibration attenuation, it is necessary to characterize their damping properties as a function of strain amplitude. This work reports the strain amplitude dependent non-linear dynamic behavior of two elastomer compounds, NBR and Neoprene, studied at various frequencies and strain amplitudes using the Fourier transform mechanical analysis (FTMA) technique, developed by us. The basic theory and experimental results are presented for a one-dimensional isothermal simple shear deformation. The Green-Rivlin constitutive equation was used to model the observed behavior. The results indicate that a complete characterization of non-linear dynamic properties is rather complex. The energy dissipation is governed, however, by a simple mechanism. It is shown that the energy dissipation is governed only by the first harmonic loss modulus term of the Green-Rivlin representation, but the energy storage is related to many material functions. An expression for the energy dissipation of a non-linear viscoelastic material is derived. It is also shown that irrespective of the material constitutive law the energy dissipation can occur only at the frequency of excitation but it can be stored in a complex manner. The results are rather generalized to show that the amplitude dependence can be modeled by a power law function. It is also shown that an examination of the stress Fourier spectra can give a quantitative indication of material non-linearity and suggest a direction for developing an adequate model of these complex materials.