Surrogate‐based Bayesian calibration of biomechanical models with isotropic material behavior

Liu, Jintian; Böl, Markus

doi:10.1002/cnm.3575

Cited by 6 publications

(2 citation statements)

References 56 publications

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“…The finite element model of the limb and socket used in this study was developed in ABAQUS using an Ogden model (N = 3) model formulation. Similar material laws are often used for describing hyperelastic behaviour in biological materials [43][44][45][46] and other hyperelastic engineering materials, 47,48 including silicone. 49 In a previously published study, we conducted a systematic analysis of the various constitutive laws suitable for modelling the mechanical properties of hyperelastic materials used in this study, and found the Ogden model (N = 3) formulation to offer the best performance.…”

Section: F I G U R Ementioning

confidence: 99%

A pneumatic reconfigurable socket for transtibial amputees

Mollaee,

Fuentes‐Aguilar,

Huegel

et al. 2024

Numer Methods Biomed Eng

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Many transtibial amputees rate the fit between their residual limb and prosthetic socket as the most critical factor in satisfaction with using their prosthesis. This study aims to address the issue of prosthetic socket fit by reconfiguring the socket shape at the interface of the residual limb and socket. The proposed reconfigurable socket shifts pressure from sensitive areas and compensates for residual limb volume fluctuations, the most important factors in determining a good socket fit. Computed tomography scan images are employed to create the phantom limb of an amputee and to manufacture the reconfigurable socket. The performance of the reconfigurable socket was evaluated both experimentally and numerically using finite element modelling. The study showed that the reconfigurable socket can reduce interface pressure at targeted areas by up to 61%.

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Section: F I G U R Ementioning

confidence: 99%

A pneumatic reconfigurable socket for transtibial amputees

Mollaee,

Fuentes‐Aguilar,

Huegel

et al. 2024

Numer Methods Biomed Eng

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show abstract

“…Generally, local and global sensitivity analysis can be distinguished, we refer to [66] for an overview regarding global sensitivity analysis. Among others the Sobol sensitivity analysis can be used as a global approach, see [62] for a certain application. In contrast, local sensitivity analysis comprises the internal numerical differentiation (IND) and external numerical differentiation (END), [28,29].…”

Section: Identification Proceduresmentioning

confidence: 99%

Identification of the thermal conductivity tensor for transversely isotropic materials

Tröger

Hartmann

2022

GAMM-Mitteilungen

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The knowledge of the thermal conductivities is of particular interest for the thermo‐mechanical modeling of transversely isotropic composite materials. Hence, the identification of these material parameters by solving an inverse problem is significant, as they cannot be directly measured. In this study, a suitable experimental setup is presented, where infrared thermography is used to measure the surface temperatures of thin specimens. Further, a local identifiability concept is employed to study whether locally unique parameters can be obtained. This leads to a particular step‐wise identification concept. The parameter identification is performed applying a nonlinear least‐square approach and finite elements. In the step‐wise identification process the convection coefficient is required first, and, subsequently, the coefficients of the thermal conductivity tensor are determined. Due to the step‐wise identification, the uncertainties of previously identified parameters have to be considered in the subsequent identification steps. The resulting uncertainties are estimated using the Gaussian error propagation concept. It turns out that the thermal conductivities of transversely isotropic materials are generally identifiable from surface temperature data. Furthermore, since all uncertainties have an essential influence on the results of real numerical simulations, their error propagation should be considered in resulting boundary‐value problems. Thus, the uncertainty quantification is demonstrated by a validation experiment.

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Comparing frequentist and Bayesian uncertainty quantification in two‐step constitutive model calibration

Tröger,

Römer,

Hartmann

2024

Proc Appl Math and Mech

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The calibration of constitutive models using experimental observations is a well‐established task in computational solid mechanics. Especially for complex constitutive models, multistep calibrations are regularly applied. While this approach is advantageous for reducing the complexity of the calibration problem, the quantification of parameter uncertainties becomes more challenging. In this study, we perform two‐step statistical parameter inference for an elasto‐plastic constitutive model utilizing a frequentist approach and Bayesian inference. The uncertainties are quantified by different methods, in particular, we compare an asymptotic normality analysis and Gaussian error propagation in the frequentist setting with sampling‐based Bayesian inference. Although frequentist and Bayesian parameter inference differ significantly in the way parameters are calibrated, both methods yield similar estimates. Additionally, the uncertainties quantified by asymptotic normality considerations and Gaussian error propagation are quite similar. However, the uncertainties of the elasticity parameters in the frequentist approach are found to be significantly smaller compared to Bayesian inference, due to the underlying approximations in the frequentist setting. Thus, uncertainties can be estimated in both settings, but it is crucial to be aware of the inherent assumptions and simplifications when interpreting the results.

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Surrogate‐based Bayesian calibration of biomechanical models with isotropic material behavior

Cited by 6 publications

References 56 publications

A pneumatic reconfigurable socket for transtibial amputees

A pneumatic reconfigurable socket for transtibial amputees

Identification of the thermal conductivity tensor for transversely isotropic materials

Comparing frequentist and Bayesian uncertainty quantification in two‐step constitutive model calibration

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