Evaluation of fundamental viscoelastic functions by a nonlinear viscoelastic model

Abstract

In this work, a new constitutive equation for the description of the nonlinear viscoelastic response of polymeric materials is presented, by proposing modifications on a model developed in previous works. This time-dependent equation has been derived on the basis of transient model, and a new assumption regarding the kinetics of active molecular chains due to the imposed deformation. The present treatment was proved to be more flexible, given that it contains a relaxation function that has been derived by considering, instead of first-order kinetics, a fractional derivative that controls the rate of molecular chain detachment from their junctions. It has been further explored that the potential of this equation to be employed for the evaluation of the dynamic modulus master curve, once the experimental data of the compliance modulus of a polymeric structure have been matched.

Limit State and Creep Behaviour of High-Density Polyethylene Geocell

“…The model determines strain rate, ̇t , as a function of deviatoric stress, and fits model constants using test results. Other models, such as viscoelastic [35], viscoplastic [19,36], and viscoelastic-viscoplastic models [37], are developed in terms of the behaviour of HDPE, loading scenarios and problems to resolve. A more generalised three-parameter creep model, known as the Bailey-Norton law [38,39], has been adopted broadly for modelling the primary creep and secondary creep as well as combined primary and secondary creeps of various materials.…”

The effectiveness of interconversion methods based on the distributed nature of polymeric structure

“…The mathematical and physical basis for an interconversion between various viscoelastic material functions has been the subject of numerous works. [ 2,7,9‐14 ] Park and Schapery [ 2,3 ] evaluated the convolution integral analytically by expressing both the source and the target function in Prony series to obtain the system of equations for the unknown coefficients of Prony series. Sorvari and Malinen [ 13 ] studied three different interconversion methods in order to determine creep compliance D(t)from relaxation test, E(t).…”