A fractional model with parallel fractional Maxwell elements for amorphous thermoplastics

作者：Lei, Dong; Liang, Yingjie; Xiao, Rui^*

来源：Physica A: Statistical Mechanics and Its Applications , 2018, 490: 465-475.

DOI：10.1016/j.physa.2017.08.037

• Fractional calculus
• Viscoelastic
• Thermoplastic
• Mittag-Leffler

We develop a fractional model to describe the thermomechanical behavior of amorphous thermoplastics. The fractional model is composed of two parallel fractional Maxwell elements. The first fractional Maxwell model is used to describe the glass transition, while the second component is aimed at describing the viscous flow. We further derive the analytical solutions for the stress relaxation modulus and complex modulus through Laplace transform. We then demonstrate the model is able to describe the master curves of the stress relaxation modulus, storage modulus and loss modulus, which all show two distinct transition regions. The obtained parameters show that the modulus of the two fractional Maxwell elements differs in 2-3 orders of magnitude, while the relaxation time differs in 7-9 orders of magnitude. Finally, we apply the model to describe the stress response of constant strain rate tests. The model, together with the parameters obtained from fitting the master curve of stress relaxation modulus, can accurately predict the temperature and strain rate dependent stress response.

• 出版日期2018-1-15
• 单位河海大学