The application of a novel variable-order fractional calculus on rheological model for viscoelastic materials

Han, Baozhi; Yin, Deshun; Gao, Yunfei

doi:10.1080/15376494.2023.2283126

Mechanics of Advanced Materials and Structures

2023

DOI: 10.1080/15376494.2023.2283126

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The application of a novel variable-order fractional calculus on rheological model for viscoelastic materials

Baozhi Han,

Deshun Yin,

Yunfei Gao

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2024

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Cited by 5 publications

References 52 publications

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A thermodynamically‐based fractional model combined viscoelastic‐viscoplastic‐ductile damage with application to fiber‐reinforced polymer composites

Han,

Yin,

Qin

et al. 2024

Polymer Composites

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A thermodynamically‐based fractional viscoelastic‐viscoplastic‐damage constitutive model combined with continuous damage mechanics (CDM) theory was established, in order to describe the rate‐dependent nonlinear behavior of fiber‐reinforced polymer composites (FRPCs). The fractional Helmholtz free energy consists of four contributions: viscoelastic (VE), viscoplastic (VP), hardening and damage, in which the VE and VP parts are constructed by fractional Zener and Scott‐Blair (SB) element forms respectively. The constitutive equation is obtained through Helmholtz free energy for the fractional Zener model, and plastic flow and hardening evolution law are all derived in the process. The ductile damage, coupled to both VE and VP free energy parts, is introduced through fractional damage energy release rates to model the degradation of material properties. The corresponding strain energy release rate and dissipation contributions are also derived. The fractional implicit time integration algorithms of proposed model are presented. The model is applied to validate tests of FRPCs under various loading conditions. The model validation and comparison are presented by simulating experimental data and existing models in the literature. And the corresponding evolution of dissipated energy is discussed to further valid the characterization ability of the model.Highlights A thermodynamical fractional constitutive model was developed for FRPCs. The Helmholtz free‐energy potential for fractional Zener model is adopted. The physical significance of fractional order parameters is explored. Fractional implicit integration algorithm of proposed model is implemented. The validation and comparison of the model are presented under various loads.

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A thermodynamically‐based fractional model combined viscoelastic‐viscoplastic‐ductile damage with application to fiber‐reinforced polymer composites

Han,

Yin,

Qin

et al. 2024

Polymer Composites

View full text Add to dashboard Cite

show abstract

Microbiology-inspired nonlinear variable-order fractional model for amorphous glassy polymer

Cai,

Wang,

Zhang

et al. 2024

Acta Mech

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On variable-order fractional linear viscoelasticity

Giusti,

Colombaro,

Garra

et al. 2024

Fract Calc Appl Anal

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A generalization of fractional linear viscoelasticity based on Scarpi’s approach to variable-order fractional calculus is presented. After reviewing the general mathematical framework, a variable-order fractional Maxwell model is analysed as a prototypical example for the theory. Some physical considerations are then provided concerning the fractionalisation procedure and the choice of the transition functions. Lastly, the material functions for the considered model are derived and numerically evaluated for exponential-type and Mittag-Leffler-type order functions.

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The application of a novel variable-order fractional calculus on rheological model for viscoelastic materials

Cited by 5 publications

References 52 publications

A thermodynamically‐based fractional model combined viscoelastic‐viscoplastic‐ductile damage with application to fiber‐reinforced polymer composites

A thermodynamically‐based fractional model combined viscoelastic‐viscoplastic‐ductile damage with application to fiber‐reinforced polymer composites

Microbiology-inspired nonlinear variable-order fractional model for amorphous glassy polymer

On variable-order fractional linear viscoelasticity

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