Dielectric elastomers are employed on a wide variety of adaptive structures. Many of these soft elastomers exhibit significant rate-dependencies in their response. Accurately quantifying this viscoelastic behavior is non-trivial and in many instances a nonlinear modeling framework is required. Fractional-order operators have been applied to modeling viscoelastic behavior for many years, and recent research has shown fractional-order methods to be effective for nonlinear frameworks. This implementation can become computationally expensive to achieve an accurate approximation of the fractional-order derivative. In this paper, we demonstrate the effectiveness of using quadrature techniques in approximating the Riemann-Liouville definition for fractional derivatives in the context of developing a nonlinear viscoelastic model.
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Numerical Techniques to Model Fractional-Order Nonlinear Viscoelasticity in Soft Elastomers
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Miles, P, Pash, G, Oates, W, & Smith, RC. "Numerical Techniques to Model Fractional-Order Nonlinear Viscoelasticity in Soft Elastomers." Proceedings of the ASME 2018 Conference on Smart Materials, Adaptive Structures and Intelligent Systems. Volume 1: Development and Characterization of Multifunctional Materials; Modeling, Simulation, and Control of Adaptive Systems; Integrated System Design and Implementation. San Antonio, Texas, USA. September 10–12, 2018. V001T03A021. ASME. https://doi.org/10.1115/SMASIS2018-8102
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