A variable order fractional constitutive model of the viscoelastic behavior of polymers. (July 2019)

• Record Type: Journal Article
• Authors: Meng, Ruifan; Yin, Deshun; Drapaca, Corina S.
• Is Part Of: International journal of non-linear mechanics. Volume 113(2019)
• Page Start: 171
• Page End: 177
• Publication Date: 2019-07
• Subjects: Polymers -- Viscoelasticity -- Fractional derivatives of variable order -- Constitutive equation; Nonlinear mechanics -- Periodicals; Mécanique non linéaire -- Périodiques; Nonlinear mechanics; Periodicals; 531
• DOI: 10.1016/j.ijnonlinmec.2019.04.002
• Languages: English
• ISSNs: 0020-7462

Abstract

Abstract: The multiple timescale evolution of polymers' microstructure due to an applied load is a well-known challenge in building models that accurately predict its mechanical behavior during deformation. Here, a constitutive model involving a variable order fractional derivative with piecewise definition is presented to describe the viscoelasticity of polymers under the condition of uniaxial loading at constant strain rates. It is shown that our model requires three parameters for small strains while five parameters are defined for large deformations. By comparing the predictions made by the proposed model with published experimental data and an existing model for polymers, we demonstrate that our model has higher accuracy while it benefits from its simple form of linearly decreasing order function to predict large deformations. An illustration based on the mechanism of molecular chain resistance indicates that the hardening process and the rate dependence of polymers are captured by the variation of fractional order. We conclude that the evolution of microstructure and mechanical properties of polymers during deformation is well represented by the variable order fractional constitutive model. Highlights: A variable order fractional viscoelastic model is proposed for polymers. The parameters are discussed at both small strains and large deformations. The decreasing order function is shown to predict the deformation of polymers. The model is applicable in various time-dependent cases of viscoelastic materials.