Aspects on viscoelasticity modeling of HDPE using fractional derivatives: Interpolation procedures and efficient numerical scheme

Abstract

Among the wide range of structural polymers currently available, this work deals with high-density polyethylene (HDPE). The typical viscoelastic behavior of this material is not trivial to model and has already been investigated by many authors. We employ the fractional Zener model to fit our experimental creep results of HDPE evaluated at different stress levels. This model produces fractional constitutive equations with excellent curve-fitting properties and fewer parameters to be identified in relation to traditional models. The results are compared with those ones provided by the application of the Prony series method. The first novelty of this paper is the application of the time-stress equivalence principle (TSEP), coupled to the fractional model, to estimate creep at intermediate stress levels, that in turn, were not measured experimentally but lie within the stress range used to calibrate the model. We compare the results provided by this method with those based on linear interpolation of the parameters. Although there is clear benefits requiring fewer parameters, fractional derivatives render costly computations due to their history memory. To cope with this, we propose a new algorithm, called GPE, which shows a compromise between enhanced efficiency and accuracy when compared with other proposals of the literature. These features are verified with simulations for simple functions, and a long term creep test with the fractional Zener model. The combined application of fractional derivatives, TSEP and the new GPE algorithm results in a novel efficient and effective alternative to account for the creep modeling of HDPE.