Modeling of elastomeric materials using nonlinear fractional derivative and continuously yielding friction elements

A model of the one-dimensional dynamic behavior of elastomeric materials is developed based on a previously existing model. An initial model consisted of nonlinear multiple anelastic displacement fields in parallel with discrete friction elements. The motivation for the development of a new model is reduction of the number of parameters needed to accurately capture material behavior. A new element, a "continuously yielding element," is developed, which conceptually represents a distribution of parallel friction elements. This element replaces the entire collection of discrete friction elements used in the initial model. In addition, a linear fractional derivative anelastic displacement field element replaces the multiple linear anelastic displacement field elements used in the older model. Finally, nonlinearity is introduced into the fractional derivative anelastic displacement field element, in an attempt to capture observed amplitude dependence of storage and loss moduli at higher amplitudes. The different parts of the new model are first compared individually to those of the initial model then combined and compared as an integrated whole. The new model captures the frequency and amplitude variation of the storage and loss moduli of the material better than the initial model, while the total number of parameters is reduced to seven from sixteen. (C) 2004 Elsevier Ltd. All rights reserved.