A Bayesian approach to selecting hyperelastic constitutive models of soft tissue

Madireddy, Sandeep; Sista, Bhargava; Vemaganti, Kumar

doi:10.1016/j.cma.2015.03.012

Cited by 81 publications

(47 citation statements)

References 47 publications

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“…Kaipio and Somersalo 2006;Rappel et al 2016 and the results section of this contribution). On the other hand, if the number of measurement data is large, the influence of the prior decreases (Madireddy et al 2015). The noise around the known theoretical response f (x,t) is independent of f (x,t) (Calvetti and Somersalo 2007).…”

Section: Bayes' Theoremmentioning

confidence: 99%

“…the prior). The influence of this prior distribution can influence the identified parameter values significantly, but its influence decreases for an increasing number of measurement data (Madireddy et al 2015;Rappel et al 2016). …”

Section: Introductionmentioning

confidence: 99%

“…Some examples are the studies of Madireddy et al (2015) for hyperelastic constitutive models for tissue, Oden et al (2013) for phenomenological models for tumour growth, Chiachío et al (2015) for models of damage progression in composites due to fatigue, and Babuška et al (2016) for fatigue descriptions of metals. Model selection is however out of the scope of the current study.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Bayes' Theoremmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Bayesian inference to identify parameters in viscoelasticity

Rappel

Beex

Bordas

2017

Mech Time-Depend Mater

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“…Based on the mean values derived at the first step, the goal of the second step is to identify the probability distributions that the random model parameters follow. For the nonlinear shear modulus (2.15), we define the variance 5) and, similarly, for every random constant coefficient, Cp, p = 1, · · · , n, the standard deviation is…”

Section: (A) Calibration Of Random Field Parametersmentioning

confidence: 99%

“…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].…”

Section: Introductionmentioning

confidence: 99%

Stochastic isotropic hyperelastic materials: constitutive calibration and model selection

2018

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Biological and synthetic materials often exhibit intrinsic variability in their elastic responses under large strains, owing 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.

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Closed‐form stress solutions for incompressible visco‐hyperelastic solids in uniaxial extension

Kossa

2017

Z Angew Math Mech

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This paper is concerned with the theory of incompressible visco-hyperelastic solids. Closed-form stress solutions are derived for five different visco-hyperelastic material models in uniaxial extension. Two loading scenarios are considered: uniaxial extension with constant true strain-rate; uniaxial extension with constant engineering strain-rate. The obtained stress solutions are expressed using only elementary functions, when the applied stretch is linear in the true strain. However, for the constant engineering strain-rate case, all the solutions are expressed using special functions, even for the very simple Hencky's hyperelastic material model. The novel solutions can be used to improve the performance and accuracy of the parameter-fitting procedure of a particular visco-hyperelastic solid. In addition, the closed-form expressions for the stresses may serve reference solution for benchmark problems.

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A Bayesian approach to selecting hyperelastic constitutive models of soft tissue

Cited by 81 publications

References 47 publications

Bayesian inference to identify parameters in viscoelasticity

Bayesian inference to identify parameters in viscoelasticity

Stochastic isotropic hyperelastic materials: constitutive calibration and model selection

Closed‐form stress solutions for incompressible visco‐hyperelastic solids in uniaxial extension

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