A Tutorial on Bayesian Inference to Identify Material Parameters in Solid Mechanics

Rappel, Hussein; Beex, Lars; Hale, Jack; Noels, Ludovic; Bordas, Stéphane

doi:10.1007/s11831-018-09311-x

Cited by 103 publications

(53 citation statements)

References 47 publications

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“…• The homogenization on the aggregate of pseudo-grains, ω (k) (k = 1, 2, ...) is then achieved using Voigt strain concentration tensor (13), in which case the set of Eqs.…”

Section: Mfh For Multi-phase Composite Materialsmentioning

confidence: 99%

“…The latter approach is chosen in the paper, and a NNW is trained by the twostep MFH for different sets of micro-structure geometrical and material parameters, and for different loading directions. The likelihood function is then constructed by considering Gaussian noise [11][12][13] as an error function [15] evaluated from the experimental observation on 40% of weight GF reinforced PA06 (PA06-GF40) coupon tests. The BI is then conducted using a Metropolis-Hastings (MCMC) random walk during which the likelihood is evaluated using the NNW as surrogate.…”

Section: Introductionmentioning

confidence: 99%

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Bayesian inference of non-linear multiscale model parameters accelerated by a Deep Neural Network

Zulueta

Major

et al. 2020

Computer Methods in Applied Mechanics and Engineering

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We develop a Bayesian Inference (BI) of a non-linear multiscale model and material parameters using experimental composite coupons tests as observation data. In particular we consider non-aligned Short Fibers Reinforced Polymer (SFRP) as a composite material system and Mean-Field Homogenization (MFH) as a multiscale model. Although MFH is computationally efficient, when considering non-aligned inclusions, the evaluation cost of a non-linear response for a given set of model and material parameters remains too prohibitive to be coupled with the sampling process required by the BI. Therefore, a Neural-Networktype (NNW) is first trained using the MFH model, and is then used as a surrogate model during the BI process, making the identification process affordable.

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“…• The homogenization on the aggregate of pseudo-grains, ω (k) (k = 1, 2, ...) is then achieved using Voigt strain concentration tensor (13), in which case the set of Eqs.…”

Section: Mfh For Multi-phase Composite Materialsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Bayesian inference of non-linear multiscale model parameters accelerated by a Deep Neural Network

Zulueta

Major

et al. 2020

Computer Methods in Applied Mechanics and Engineering

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show abstract

“…Once the simplest and most representative model has been identified, e.g. using Bayesian inference, 48 material parameters can be estimated. If the information available is sparse and scarce, a Bayesian approach may be particularly suitable, 49,50 which can also be applied to anisotropic and inhomogeneous materials.…”

Section: Exploiting Simulations To Anticipate Pitfallsmentioning

confidence: 99%

<p>Robotically Steered Needles: A Survey of Neurosurgical Applications and Technical Innovations</p>

Audette¹,

Bordas²,

Blatt³

2020

RSRR

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This paper surveys both the clinical applications and main technical innovations related to steered needles, with an emphasis on neurosurgery. Technical innovations generally center on curvilinear robots that can adopt a complex path that circumvents critical structures and eloquent brain tissue. These advances include several needle-steering approaches, which consist of tip-based, lengthwise, base motion-driven, and tissue-centered steering strategies. This paper also describes foundational mathematical models for steering, where potential fields, nonholonomic bicycle-like models, spring models, and stochastic approaches are cited. In addition, practical path planning systems are also addressed, where we cite uncertainty modeling in path planning, intraoperative soft tissue shift estimation through imaging scans acquired during the procedure, and simulation-based prediction. Neurosurgical scenarios tend to emphasize straight needles so far, and span deep-brain stimulation (DBS), stereoelectroencephalography (SEEG), intracerebral drug delivery (IDD), stereotactic brain biopsy (SBB), stereotactic needle aspiration for hematoma, cysts and abscesses, and brachytherapy as well as thermal ablation of brain tumors and seizure-generating regions. We emphasize therapeutic considerations and complications that have been documented in conjunction with these applications.

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“…Starting from the work of [21], many works identified the parameters of material models through BI: elasticity constants of glass-fiber reinforced epoxy [22] and of carbon-epoxy unidirectional laminates [23] were inferred through vibration tests, and elasticity constants of graphite-epoxy laminates were identified from the displacement field in [24] through static tests; in the non-linear range, elasto-perfectly plastic model and cohesive zone parameters were inferred in [25], elasto-plastic material model parameters in [26,27], visco-elasticity constants in [28,29] and a hyperelastic model and its parameters in [30]; spatially varying, under the form of embedded inclusions, elasticity constants were identified in [31]; the list being non-exhaustive.…”

Section: Introductionmentioning

confidence: 99%

Bayesian identification of Mean-Field Homogenization model parameters and uncertain matrix behavior in non-aligned short fiber composites

Mohamedou

Zulueta

Chung

et al. 2019

Composite Structures

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We present a stochastic approach combining Bayesian Inference (BI) with homogenization theories in order to identify, on the one hand, the parameters inherent to the model assumptions and, on the other hand, the composite material constituents behaviors, including their variability. In particular, we characterize the model parameters of a Mean-Field Homogenization (MFH) model and the elastic matrix behavior, including the inherent dispersion in its Young's modulus, of non-aligned Short Fibers Reinforced Polymer (SFRP) composites. The inference is achieved by considering as observations experimental tests conducted at the SFRP composite coupons level. The inferred model and material law parameters can in turn be used in Mean-Field Homogenization (MFH)-based multi-scale simulations and can predict the confidence range of the composite material responses.

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A Tutorial on Bayesian Inference to Identify Material Parameters in Solid Mechanics

Cited by 103 publications

References 47 publications

Bayesian inference of non-linear multiscale model parameters accelerated by a Deep Neural Network

Bayesian inference of non-linear multiscale model parameters accelerated by a Deep Neural Network

<p>Robotically Steered Needles: A Survey of Neurosurgical Applications and Technical Innovations</p>

Bayesian identification of Mean-Field Homogenization model parameters and uncertain matrix behavior in non-aligned short fiber composites

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