Constitutive modeling of stress relaxation for fabric reinforced rubber composites

Establishing an unsteady fractional order Zener model with degradation parameters has significant meaning for predicting stress relaxation of fabric reinforced rubber composites. Based on the experimental results, an integer order Zener model was deduced to demonstrate the stress relaxation behaviors of fabric reinforced rubber composites and pure rubber. Due to the limitations, however, the integer order Zener model could not explain the stress relaxation behavior of the fabric reinforced rubber composites (the FRR) very well. Therefore, a Zener model was developed based on the viscoelasticity theory and the fractional calculus theory to characterize the stress relaxation behavior, but errors still existed in the initial and final stages. With more reasonable physical interpretation, an unsteady fractional order Zener model degraded by parametric aging with 7 parameters is proposed in this paper to accurately capture the stress relaxation behavior of the FRR, whose correlation coefficient is over 99.99%. The parameter sensitivities of the seven-parameter model were analyzed. Present study may provide a critical step for designing and evaluating the fabric reinforced rubber composites.