Efficient modeling of elastomeric materials using fractional derivatives and plastic yielding

A new model is developed that captures frequency and amplitude-dependent behavior often exhibited by elastomeric materials. The new model requires substantially fewer parameters than does a recently developed model based on Nonlinear Anelastic Displacement Fields and Friction elements. A continuously yielding friction element is used to capture the amplitude dependence modulus, independent of the frequency. A linear fractional derivative model based on Anelastic Displacement Fields is used in parallel to capture the mild frequency dependence of the dynamic modulus. The model based on Nonlinear Multi Anelastic displacement field and Friction elements, which accurately captures the dynamic behavior of elastomers in a frequency range of 0.01 to 10 HZ and a strain amplitude range of 0.1% to 20%, is used to characterize the new model. The new model, featuring seven fewer parameters, predicts mechanical behavior very similar to that of its predecessor. Also, the parameters of the new model have a more direct physical interpretation than those of the original model.