Uncertainty quantification for constitutive model calibration of brain tissue

Brewick, Patrick T.; Teferra, Kirubel

doi:10.1016/j.jmbbm.2018.05.037

Cited by 23 publications

(11 citation statements)

References 78 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Assumptions (A1)-(A3) are inherited from the finite elasticity theory [21,44,54,75], while (A4) places random variables at the foundation of stochastic hyperelastic models [46,[68][69][70]. A random variable is usually described in terms of its mean value and its variance, which contains information about the range of values about the mean value [11,13,28,39,52].…”

Section: Stochastic Strain-energy Functions For Isotropic Incompressi...mentioning

confidence: 99%

“…where (R, Θ, Z) and (r, θ, z) are the cylindrical polar coordinates in the reference and current configuration, respectively, such that C ≤ R ≤ B, C and B are the inner and outer radii in the undeformed state, respectively, c = c(t) and b = b(t) = c 2 + (B 2 − C 2 ) /α are the inner and outer radius at time t, respectively, and α > 0 is a given constant. When α = 1, the time-dependent deformation (11) simplifies to that studied in [8,34,35]. The case with a time-dependent α was considered in [58].…”

Section: Radial-axial Motion Of a Cylindrical Tubementioning

confidence: 99%

“…The radial-axial motion (11) of a cylindrical tube is fully determined by the inner radius c at time t, which in turn is derived from the initial conditions. Thus, the acceleration r can be obtained in terms of the acceleration c on the inner surface.…”

Section: Radial-axial Motion Of a Cylindrical Tubementioning

confidence: 99%

See 2 more Smart Citations

Likely oscillatory motions of stochastic hyperelastic spherical shells and tubes

Mihai

Alamoudi

2021

International Journal of Non-Linear Mechanics

View full text Add to dashboard Cite

Section: Stochastic Strain-energy Functions For Isotropic Incompressi...mentioning

confidence: 99%

Section: Radial-axial Motion Of a Cylindrical Tubementioning

confidence: 99%

See 1 more Smart Citation

Likely oscillatory motions of stochastic hyperelastic spherical shells and tubes

Mihai

Alamoudi

2021

International Journal of Non-Linear Mechanics

View full text Add to dashboard Cite

“…In contrast, a stochastic hyperelastic model has parameters which are defined by probability density functions [37,[65][66][67]. Typically, each model parameter is described in terms of its mean value and its variance, which hold information regarding the range of values about the mean value [5,6,18,29,44]. Here, we construct stochastic homogeneous isotropic incompressible hyperelastic models that rely on the following assumptions [33-35, 37, 38, 40]:…”

Section: Stochastic Isotropic Incompressible Hyperelastic Modelsmentioning

confidence: 99%

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

et al. 2019

View full text Add to dashboard Cite

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 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 finite elasticity. The proposed stochastic calibration and Bayesian model selection are generally applicable to more complex tests and materials. Keywords Stochastic elasticity • Finite strain analysis • Hyperelastic material • Bayes' factor • Experiments • Probabilities "This task is made more difficult than it otherwise would be by the fact that some of the test-pieces used have to be moulded individually, and it is difficult to make two rubber specimens having identical properties even if nominally identical procedures are followed in preparing them."-R.S. Rivlin and D.W. Saunders [55]

show abstract

“…The proper randomization of Ogden's strain energy functions was first addressed in [9,10] for homogeneous materials (see also [11]), and the case of spatially dependent behaviors was treated in [12]. Studies reporting on the identification of such models can be found in, e.g., [13,14] for homogeneous biological tissues. In this context, the identification of stochastic models for anisotropic, heterogeneous nonlinear materials remain widely unexplored.…”

Section: Introductionmentioning

confidence: 99%

Stochastic modeling and identification of a hyperelastic constitutive model for laminated composites

Staber

Guilleminot

Soize

et al. 2019

Computer Methods in Applied Mechanics and Engineering

View full text Add to dashboard Cite

In this paper, we investigate the construction and identification of a new random field model for representing the constitutive behavior of laminated composites. Here, the material is modeled as a random hyperelastic medium characterized by a spatially dependent, stochastic and anisotropic strain energy function. The latter is parametrized by a set of material parameters, modeled as non-Gaussian random fields. From a probabilistic standpoint, the construction is first achieved by invoking information theory and the principle of maximum entropy. Constraints related to existence theorems in finite elasticity are, in particular, accounted for in the formulation. The identification of the parameters defining the random fields is subsequently addressed. This issue is attacked as a two-step problem where the mean model is calibrated in a first step, by imposing a match between the linearized model and nominal values proposed in the literature. The remaining parameters controlling the fluctuations are next estimated by solving an inverse problem in which principal component analysis and the maximum likelihood method are combined. The whole framework is illustrated considering an experimental database where multi-axial measurements are performed on a carbonepoxy laminate. This work constitutes a first step towards the development of an integrated framework that will support decision making under uncertainty for the design, certification and qualification of composite materials and structures.

show abstract

Uncertainty quantification for constitutive model calibration of brain tissue

Cited by 23 publications

References 78 publications

Likely oscillatory motions of stochastic hyperelastic spherical shells and tubes

Likely oscillatory motions of stochastic hyperelastic spherical shells and tubes

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

Stochastic modeling and identification of a hyperelastic constitutive model for laminated composites

Contact Info

Product

Resources

About