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Uncertainty quantification of elastic material responses: testing, stochastic calibration and Bayesian model selection

Fitt, Danielle, Wyatt, Hayley, Woolley, Thomas and Mihai, L. Angela 2019. Uncertainty quantification of elastic material responses: testing, stochastic calibration and Bayesian model selection. Mechanics of Soft Materials
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Abstract

Motivated by the need to quantify uncertainties in the mechanical behaviour of solid materials, we perform simple uniaxial tensile tests on a manufactured rubber-like material that provide critical information regarding the variability in the constitutive responses between di�erent specimens. Based on the experimental data, we construct stochastic homogeneous hyperelastic models where the parameters are described by spatially-independent probability density functions at a macroscopic level. As more than one parametrised model is capable of capturing the observed material behaviour, we apply Bayes' theorem to select the model that is most likely to reproduce the data. Our analysis is fully tractable mathematically and builds directly on knowledge from deterministic �nite elasticity. The stochastic calibration and Bayesian model selection are generally applicable to more complex tests and materials.

Item Type: Article
Status: In Press
Schools: Engineering
Mathematics
Publisher: Springer
Date of First Compliant Deposit: 17 October 2019
Date of Acceptance: 7 October 2019
Last Modified: 28 Oct 2019 06:50
URI: http://orca.cf.ac.uk/id/eprint/126123

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