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Stochastic isotropic hyperelastic materials: constitutive calibration and model selection

Mihai, Loredana Angela, Woolley, Thomas and Goriely, Alain 2018. Stochastic isotropic hyperelastic materials: constitutive calibration and model selection. Proceedings of the Royal Society A 474 (2211) , 201708. 10.1098/rspa.2017.0858

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Biological and synthetic materials often exhibit intrinsic variability in their elastic responses under large strains, due to microstructural inhomogeneity or when elastic data are extracted from viscoelastic mechanical tests. For these materials, although hyperelastic models calibrated to mean data are useful, stochastic representations accounting also for data dispersion carry extra information about the variability of material properties found in practical applications. We combine finite elasticity and information theories to construct homogeneous isotropic hyperelastic models with random field parameters calibrated to discrete mean values and standard deviations of either the stress-strain function or the nonlinear shear modulus, which is a function of the deformation, estimated from experimental tests. These quantities can take on different values, corresponding to possible outcomes of the experiments. As multiple models can be derived that adequately represent the observed phenomena, we apply Occam’s razor by providing an explicit criterion for model selection based on Bayesian statistics. We then employ this criterion to select a model among competing models calibrated to experimental data for rubber and brain tissue under single or multiaxial loads.

Item Type: Article
Date Type: Publication
Status: Published
Schools: Mathematics
Publisher: The Royal Society
ISSN: 1364-5021
Date of First Compliant Deposit: 16 February 2018
Date of Acceptance: 16 February 2018
Last Modified: 15 Mar 2020 14:11

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