Prediction of apparent properties with uncertain material parameters using high‐order fictitious domain methods and PGD model reduction

Legrain, Grégory; Chevreuil, Mathilde; Takano, Naoki

doi:10.1002/nme.5289

Cited by 6 publications

(4 citation statements)

References 79 publications

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“…Because we proposed framework which could update the range of the stochastic prediction, measurement of the mechanical properties for the drilling direction of jawbone could be the crucial future work. Though the proposed computational method is focused on small range of uncertainty, in the case of large uncertainty, the proper generalized decomposition (PGD) technique [Legrain et al, 2016] would be useful. Third, direct validation of numerical results is very difficult, however, indirect verification of the numerical analysis can be possible by applying the drilling force to our force-sensitive device.…”

Section: Discussionmentioning

confidence: 99%

Stochastic Multi-Scale Finite Element Analysis of the Drilling Force of Trabecular Bone During Oral Implant Surgery

Tawara

Takano

Kinoshita

et al. 2016

Int. J. Appl. Mechanics

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Int. J. Appl. Mechanics Downloaded from www.worldscientific.com by FUDAN UNIVERSITY on 11/26/16. For personal use only. D. Tawara et al. value and 50% and 90% probability results suggested prominent differences in drilling properties. This information enables dentists to develop a skillful surgical technique. Keywords: Oral implant; drilling force; mandibular trabecular bone; stochastic homogenization method; finite element analysis; bone quality. 1650075-2 Int. J. Appl. Mechanics Downloaded from www.worldscientific.com by FUDAN UNIVERSITY on 11/26/16. For personal use only.

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Section: Discussionmentioning

confidence: 99%

Stochastic Multi-Scale Finite Element Analysis of the Drilling Force of Trabecular Bone During Oral Implant Surgery

Tawara

Takano

Kinoshita

et al. 2016

Int. J. Appl. Mechanics

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“…Let us also mention that not all the difficulties are caused by the meshing process: usual B-REP CAD description only describes the surface of the domains, and commonly contains hole, overlap and badly oriented surfaces [11]. Fictitious domain methods can be very robust in that regard, also simplifying the treatment of image-based applications [12,13,14,15]. The flexibility and robustness of the method regarding geometrical as-Figure 1: Setup of a mechanical problem using fictitious domain methods.…”

Section: Introductionmentioning

confidence: 99%

“…Compute Q according to (15) 23 end Algorithm 3: Quality oriented quadrature strategy from [29]. Note that in this contribution, the test on line 8 was replaced by "Q > Q lim and min {w q } ≥ 0" as we are interested in positive quadrature rules.…”

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confidence: 99%

Non-negative moment fitting quadrature rules for fictitious domain methods

Legrain

2021

Computers & Mathematics with Applications

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Fictitious domain methods enable to solve physical problems on unfitted grids, thereby avoiding time-consuming and error prone meshing phases. However, an accurate integration of the weak formulation is still mandatory, leading to the need for efficient quadrature strategies in the elements that are partially located in the physical domain. Various methodologies have been proposed to this end. Among them, the design of element-specific moment-fitting quadrature rules seems promising. However, some of the resulting weights are usually negative and the points located out of the domain which may lead to a lack quadrature stability. In this contribution, we aim to construct quadrature rules whose weights are all positive and points all located in the physical domain. Such rules can be constructed based on a non-negative least square resolution of the moment-fitting equations. The resulting quadrature formulas are compared to empirical quadrature rules and different variants of classical moment-fitting quadrature rules in both 1D and 2D. Benchmarks show that non-negative moment-fitting quadrature rules are robust and efficient although their setup cost can be significantly higher than classical moment-fitting. Finally, their application to linear elastic and small-strain elasto-plastic problems highlight their robustness for engineering applications.

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“…The random processes are expanded along a basis of random parameters. The proper generalized decomposition spectral method was used to represent the result in an explicit form, using a finite number of random variables (Legrain et al, 2017).…”

Section: Introductionmentioning

confidence: 99%

Influence of higher orders of Neumann expansion on accuracy of stochastic linear elastic finite element method with random physical parameters

Degeneve

Takano²

2020

Mechanical Engineering Letters

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The objective of this study is to quantify the influence of higher orders of expansion in the formulation of stochastic finite elements method on the linear elastic response in 2-dimensional problems with random physical parameters in the left hand side term. Neumann expansion was used to get an explicit expression of the result. Young's modulus was considered as a random variable following normal distribution. The coefficient of variance (COV) of this input parameter ranged in this study up to 0.3 (30%), and mainly 20% of COV was analyzed. The displacement was selected as the quantity of interest. The difference in distribution function of the displacement for different orders of expansion was observed in the tail distribution. A fundamental example revealed the limitation of the applicability of first, second and third orders being approximately 3%, 12% and 20% of COV of input parameter. In the analysis of 2-phase composite material, the influence of geometrical random morphology was larger than that of physical parameter, but the latter was not negligible in the microscopic response.

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Prediction of apparent properties with uncertain material parameters using high‐order fictitious domain methods and PGD model reduction

Cited by 6 publications

References 79 publications

Stochastic Multi-Scale Finite Element Analysis of the Drilling Force of Trabecular Bone During Oral Implant Surgery

Stochastic Multi-Scale Finite Element Analysis of the Drilling Force of Trabecular Bone During Oral Implant Surgery

Non-negative moment fitting quadrature rules for fictitious domain methods

Influence of higher orders of Neumann expansion on accuracy of stochastic linear elastic finite element method with random physical parameters

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