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 different 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 Baye 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 finite elasticity. The proposed stochastic calibration and Bayesian model selection are generally applicable to more complex tests and materials.
Highlights
The study of material elastic properties has traditionally used deterministic approaches, based on ensemble averages, to quantify constitutive parameters [36]
Stochastic models were proposed for nonlinear elastic materials, where the parameters are characterised by probability distributions at a continuum level [37, 65,66,67,68,69]
In recognition of the fact that a crucial part in assessing the elasticity of materials is to quantify the uncertainties in their mechanical responses, for rubber and soft tissues under large strain deformations, explicit stochastic hyperelastic models based on datasets consisting of mean values and standard deviations were developed in [37], while statistical models derived from numerically generated data were proposed in [6, 44]
Summary
The study of material elastic properties has traditionally used deterministic approaches, based on ensemble averages, to quantify constitutive parameters [36]. These parameters can meaningfully take on different values corresponding to possible outcomes of the experiments. Stochastic models (described by a strain-energy density) were proposed for nonlinear elastic materials, where the parameters are characterised by probability distributions at a continuum level [37, 65,66,67,68,69].
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