Stochastic finite element with material uncertainties: Implementation in a general purpose simulation program

Shang, Shen; Yun, Gun Jin

doi:10.1016/j.finel.2012.10.001

Cited by 67 publications

(29 citation statements)

References 40 publications

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“…The resulting field possesses a mean ofĒ = 210 GPa, with a correlation length of cor = 20 mm, and a standard deviation of 5%. Additional details concerning the construction of such fields are provided in Shang and Yun (2013). We now hold the regularization length and spatially varying Young's modulus field fixed, and examine the fracture patterns predicted by our simulations over a sequence of increasingly refined meshes.…”

Section: Fragmentation Of a Thick Cylindermentioning

confidence: 99%

A phase-field formulation for dynamic cohesive fracture

Geelen¹,

Liu²,

Hu³

et al. 2019

Computer Methods in Applied Mechanics and Engineering

184

106

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We extend a phase-field/gradient damage formulation for cohesive fracture to the dynamic case. The model is characterized by a regularized fracture energy that is linear in the damage field, as well as non-polynomial degradation functions. Two categories of degradation functions are examined, and a process to derive a given degradation function based on a local stress-strain response in the cohesive zone is presented. The resulting model is characterized by a linear elastic regime prior to the onset of damage, and controlled strain-softening thereafter. The governing equations are derived according to macro-and microforce balance theories, naturally accounting for the irreversible nature of the fracture process by introducing suitable constraints for the kinetics of the underlying microstructural changes. The model is complemented by an efficient staggered solution scheme based on an augmented Lagrangian method. Numerical examples demonstrate that the proposed model is a robust and effective method for simulating cohesive crack propagation, with particular emphasis on dynamic fracture.

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Section: Fragmentation Of a Thick Cylindermentioning

confidence: 99%

A phase-field formulation for dynamic cohesive fracture

Geelen¹,

Liu²,

Hu³

et al. 2019

Computer Methods in Applied Mechanics and Engineering

184

106

View full text Add to dashboard Cite

show abstract

“…Regarding the sampling Janssen [18] presents a series of sampling Monte Carlo simulations to substantially reduce the number of simulations required to achieve good results. Regarding the distribution of adjustments, some authors [19,20] applied the Karhunen-Loève expansion to perform the discretization of the random field successfully. …”

Section: Discussionmentioning

confidence: 99%

Dynamic properties comparisons between experimental measurements and nondeterministic numerical models of viscoelastic sandwich beams

Filho

Barbosa

2015

MATEC Web of Conferences

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Abstract. In order to design viscoelastic sandwich structures used as passive damping treatment, many aspects should be considered. In all methods available in the literature to model Viscoelastic Materials (VEM) a crucial step is the determination of the complex modulus, usually obtained by curve fitting experimental results. Considering that dispersions are inherent to experimental tests and also those small variations in the fitted parameters lead to considerable changes on the dynamic behavior of VEMs hence a nondeterministic model seems to be more suitable than the usual deterministic ones. In that way, starting from dynamic properties of a VEM, a nondeterministic numerical model, which takes into account incertitudes in the VEM curve fitting procedure, is proposed. This model was used to evaluate the behavior of sandwich structures, showing the advantages and disadvantages of the presented methodology, comparing damping ratios and natural frequencies results of experimental tests with the ones extracted from the proposed nondeterministic numerical GHM based model, in order to establish a method to support viscoelastic sandwich beams design.

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“…Uncertainties of material properties are always assumed to follow the Gaussian distribution because of its simplicity and the lack of relevant experimental data, even though most material property distributions are non-Gaussian in nature [26,27]. The theory introduced in this case is about the probabilistic modeling of a random elasticity tensor in an orthotropic symmetric level within the framework of the maximum entropy principle under the constraint of the available information [18,19,28].…”

Section: Stochastic Processmentioning

confidence: 99%

Development of a Vibroacoustic Stochastic Finite Element Prediction Tool for a CLT Floor

et al. 2019

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Low frequency impact sound insulation is a challenging task in wooden buildings. Low frequency prediction tools are needed to access the dynamic behavior of a wooden floor in an early design phase to ultimately reduce the low frequency impact noise. However, due to the complexity of wood and different structural details, accurate vibration predictions of wood structures are difficult to attain. Meanwhile, a deterministic model cannot properly represent the real case due to the uncertainties coming from the material properties and geometrical changes. The stochastic approach introduced in this paper aims at quantifying the uncertainties induced by material properties and proposing an alternative calibration method to obtain a relative accurate result instead of the conventional manual calibration. In addition, 100 simulations were calculated in different excitation positions to assess the uncertainties induced by material properties of cross-laminated-timber A comparison between the simulated and measured results was made in order to extract the best combination of Young’s moduli and shear moduli in different directions of the CLT panel.

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Stochastic finite element with material uncertainties: Implementation in a general purpose simulation program

Cited by 67 publications

References 40 publications

A phase-field formulation for dynamic cohesive fracture

A phase-field formulation for dynamic cohesive fracture

Dynamic properties comparisons between experimental measurements and nondeterministic numerical models of viscoelastic sandwich beams

Development of a Vibroacoustic Stochastic Finite Element Prediction Tool for a CLT Floor

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