A fractional finite strain viscoelastic model of dielectric elastomer

• Published in: Applied Mathematical Modelling Vol. 100; pp. 564 - 579
• Main Authors: Zhao, DeMin, Yin, YaoDe, Liu, JianLin
• Format: Journal Article
• Language: English
• Published: New York Elsevier Inc 01.12.2021; Elsevier BV
• Subjects: Artificial muscles; Axial stress; Constitutive models; Constitutive relationships; Creep (materials); Deformation effects; Derivatives; Dielectric elastomer; Elastomers; Finite strain; Fractional viscoelastic model; Free vibration; Integrals; Mathematical models; Membranes; Nonlinear dynamics; Numerical method; Runge-Kutta method; Strain; Viscoelasticity; Nonlinear dynamics; Dielectric elastomer; Numerical method; Finite strain; Fractional viscoelastic model
• ISSN: 0307-904X; 1088-8691; 0307-904X
• DOI: 10.1016/j.apm.2021.08.023

•The constitutive model of dielectric elastomer (DE) based on fractional Kelvin-Voigt model at finite strain is developed.•The model is identified and the fractional-order element performs a feature of Non-Newtonian fluid.•Fractional dynamics system of DE is solved by a combined method of composite integration rule and Runge-Kutta approach.•A convenient method to evaluate final equilibrium location is given, which reduces the calculation amount dramatically. Dielectric elastomer (DE) is an intelligent soft material and it is regarded as one significant artificial muscle. The nonlinear large deformation, electromechanical coupling and nonlinear viscoelasticity of DE material post great challenges for constitutive modeling and the associated dynamics. Fractional viscoelasticity has encountered some successes in the dynamics of complex materials. In the current study, a 3D constitutive relation of DE based on the fractional Kelvin-Voigt viscoelastic model by considering finite strain is established. The Cauchy stress under the condition of uniaxial and biaxial stretches is derived. The fractional dynamics equations of DE membrane are also formulated based on the virtual work principle. The composite integral rule for fractional derivative and the Runge-Kutta method are combined to numerically solve the dynamics system. The constitutive model is fitted to the uniaxial and biaxial stretch experimental data, and the material parameters are obtained. Subject to a cyclic deformation, the stress-softening effect of the DE membrane is simulated. Furthermore, the dynamics responses of DE membrane are also calculated. A convenient approach is given to evaluate the equilibrium point of the system. It reveals that the model could be used to predict the creep behaviors for both free vibration and parametric excitation vibration.