Bayesian uncertainty analysis of finite deformation viscoelasticity

Miles, Paul; Hays, Michael; Smith, Ralph C.; Oates, William S.

doi:10.1016/j.mechmat.2015.07.002

Cited by 42 publications

(25 citation statements)

References 19 publications

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“…al., 10 and extend the key results using fractional order methods. The viscoelastic stress, Q ν iK , is related to an energy function which depends on a set of unknown internal strains, Γ ν iK .…”

Section: Fractional Order Viscoelasticitysupporting

confidence: 56%

“…The hyperelastic stress is most compactly determined from calculating the nominal stress from changes in a hyperelastic energy function with respect to the deformation gradient. 10 These hyperelastic stress relations are obtained from…”

Section: Nonlinear Membrane Mechanicsmentioning

confidence: 99%

“…Previous research has shown the theoretical development for both linear and nonlinear viscoelastic models. 10 Both models were derived assuming integer order calculus operators. It was found that the viscoelastic model parameters were rate dependent, following a power law trend.…”

Section: Fractional Order Viscoelasticitymentioning

confidence: 99%

“…where s iK is the hyperelastic stress from (10), s E iK is the nominal electrostrictive stress that is self-consistent with (11) and the viscoelastic stress is s V iK = ν Q ν iK . These nominal stress measures can be converted to the second Piola-Kirchhoff stress using the relations given by (3).…”

Section: Fractional Order Viscoelasticitymentioning

confidence: 99%

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Rate dependent constitutive behavior of dielectric elastomers and applications in legged robotics

et al. 2017

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Dielectric elastomers exhibit novel electromechanical coupling that has been exploited in many adaptive structure applications. Whereas the quasi-static, one-dimensional constitutive behavior can often be accurately quantified by hyperelastic functions and linear dielectric relations, accurate predictions of electromechanical, rate-dependent deformation during multiaxial loading is non-trivial. In this paper, an overview of multiaxial electromechanical membrane finite element modeling is formulated. Viscoelastic constitutive relations are extended to include fractional order. It is shown that fractional order viscoelastic constitutive relations are superior to conventional integer order models. This knowledge is critical for transition to control of legged robotic structures that exhibit advanced mobility.

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Section: Fractional Order Viscoelasticitysupporting

confidence: 56%

Section: Nonlinear Membrane Mechanicsmentioning

confidence: 99%

Section: Fractional Order Viscoelasticitymentioning

confidence: 99%

Section: Fractional Order Viscoelasticitymentioning

confidence: 99%

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Rate dependent constitutive behavior of dielectric elastomers and applications in legged robotics

et al. 2017

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“…Mehrez et al (2015) employed BI to identify the viscoelastic properties of aged and unaged asphalt. Miles et al (2015) applied BI to characterise the viscoelastic parameters of a dielectric elastomer undergoing finite deformation. Hernandez et al (2015) employed the Bayesian approach for the probabilistic identification of five viscoelastic parameters.…”

Section: Introductionmentioning

confidence: 99%

Bayesian inference to identify parameters in viscoelasticity

Rappel

Beex

Bordas

2017

Mech Time-Depend Mater

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This contribution discusses Bayesian inference (BI) as an approach to identify parameters in viscoelasticity. The aims are (i) to show that the prior has a substantial influence for viscoelasticity, (ii) to show that this influence decreases for an increasing number of measurements and (iii) to show how different types of experiments influence the identified parameters and their uncertainties. The standard linear solid model is the material description of interest and a relaxation test, a constant strain-rate test and a creep test are the tensile experiments focused on. The experimental data are artificially created, allowing us to make a one-to-one comparison between the input parameters and the identified parameter values. Besides dealing with the aforementioned aims, we believe that this contribution forms a comprehensible start for those interested in applying BI in viscoelasticity.

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