Bayesian calibration of hyperelastic constitutive models of soft tissue

A Bayesian approach to selecting hyperelastic constitutive models of soft tissue

“…However, the evidence value for Ogden (N = 1) is higher than Ogden (N = 2, 3), which means that the latter models overfit the data. (This is confirmed by the flat log-likelihood plots for Ogden (N = 2, 3) in [56]). Thus, there is no parsimonious model among the candidates; they either under-fit the data (as seen from the model fit in Fig.…”

“…Additionally we look at the landscape of the likelihood function (based on the work by [56]) as a crucial criterion to consider in the model selection process. For Data A, The log-likelihood function shows distinct peaks for the Mooney-Rivlin, exponential, and Ogden (N = 1, 2), but shows a relatively flat likelihood surface for Ogden (N = 3).…”

“…As with Data B discussed above, the likelihood plots confirm the overfitting. These are however not shown here for the sake of brevity, but may be found in [56].…”

Stochastic isotropic hyperelastic materials: constitutive calibration and model selection

“…To find Cp , we then need to minimise the residual 6) between the standard deviation (3.5) and the associated data {ds} s=1,··· ,m at the prescribed stretches {as} s=1,··· ,m . Before we do so, we fix the value of the stretch parameter to a particular value a 0 > 0 that is used for calibration.…”

“…Further developments in the stochastic modelling of heterogeneous solids were reviewed in [3]. Recently, there has been a growing interest in probability and statistical techniques for engineering and biomedical applications, where the calibration of models using available data and the quantification of uncertainties in model parameters are of utmost importance [4][5][6]. There are, however, many challenges introduced by the consideration and quantification of uncertainties in mathematical models, and their use in making predictions, some of which are discussed in [7][8][9][10][11][12].…”