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14 pages, 2982 KiB

Open AccessArticle

A Stochastic Damage Model for Bond Stress-Slip Relationship of Rebar-Concrete Interface under Monotonic Loading

by Xiaoyong Lv, Zhiwu Yu, Zhi Shan and Ju Yuan

Materials 2019, 12(19), 3151; https://doi.org/10.3390/ma12193151 - 26 Sep 2019

Cited by 9 | Viewed by 2536

Abstract

The stochastic bond stress-slip behavior is an essential topic for the rebar-concrete interface. However, few theoretical models incorporating stochastic behavior in current literature can be traced. In this paper, a stochastic damage model based on micro-mechanical approach for bond stress-slip relationship of the [...] Read more.

The stochastic bond stress-slip behavior is an essential topic for the rebar-concrete interface. However, few theoretical models incorporating stochastic behavior in current literature can be traced. In this paper, a stochastic damage model based on micro-mechanical approach for bond stress-slip relationship of the interface under monotonic loading was proposed. In order to describe the mechanical behaviors of the rebar-concrete interface, a microscopic damage model was proposed. By introducing a micro-element consists of parallel spring element, friction element and a switch element, the model is formulated. In order to reflect the randomness of the bond stress-slip behavior contributed by the micro-fracture in the interface, a series of paralleled micro-elements are adopted with the failure threshold of individual spring element is set as a random variable. The expression of both mean and variance for the bond stress-slip relationship was derived based on statistical damage mechanics. Furthermore, by utilizing a search heuristic global optimization algorithm (i.e., a genetic algorithm), parameters of the proposed model are able to be identified from experimental results, which a lognormal distribution has adopted. The prediction was verified against experimental results, and it reveals that the proposed model is capable of capturing the random nature of the micro-structure and characterizing the stochastic behavior. Full article

(This article belongs to the Special Issue Randomness and Uncertainty)

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22 pages, 1094 KiB

Open AccessArticle

Mesh-Based and Meshfree Reduced Order Phase-Field Models for Brittle Fracture: One Dimensional Problems

by Ngoc-Hien Nguyen, Vinh Phu Nguyen, Jian-Ying Wu, Thi-Hong-Hieu Le and Yan Ding

Materials 2019, 12(11), 1858; https://doi.org/10.3390/ma12111858 - 8 Jun 2019

Cited by 10 | Viewed by 3727

Abstract

Modelling brittle fracture by a phase-field fracture formulation has now been widely accepted. However, the full-order phase-field fracture model implemented using finite elements results in a nonlinear coupled system for which simulations are very computationally demanding, particularly for parametrized problems when the randomness [...] Read more.

Modelling brittle fracture by a phase-field fracture formulation has now been widely accepted. However, the full-order phase-field fracture model implemented using finite elements results in a nonlinear coupled system for which simulations are very computationally demanding, particularly for parametrized problems when the randomness and uncertainty of material properties are considered. To tackle this issue, we present two reduced-order phase-field models for parametrized brittle fracture problems in this work. The first one is a mesh-based Proper Orthogonal Decomposition (POD) method. Both the Discrete Empirical Interpolation Method (DEIM) and the Matrix Discrete Empirical Interpolation Method ((M)DEIM) are adopted to approximate the nonlinear vectors and matrices. The second one is a meshfree Krigingmodel. For one-dimensional problems, served as proof-of-concept demonstrations, in which Young’s modulus and the fracture energy vary, the POD-based model can speed up the online computations eight-times, and for the Kriging model, the speed-up factor is 1100, albeit with a slightly lower accuracy. Another merit of the Kriging’s model is its non-intrusive nature, as one does not need to modify the full-order model code. Full article

(This article belongs to the Special Issue Randomness and Uncertainty)

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19 pages, 2558 KiB

Open AccessArticle

Quantification of Uncertainties on the Critical Buckling Load of Columns under Axial Compression with Uncertain Random Materials

by Hai-Bang Ly, Christophe Desceliers, Lu Minh Le, Tien-Thinh Le, Binh Thai Pham, Long Nguyen-Ngoc, Van Thuan Doan and Minh Le

Materials 2019, 12(11), 1828; https://doi.org/10.3390/ma12111828 - 5 Jun 2019

Cited by 43 | Viewed by 5031

Abstract

This study is devoted to the modeling and simulation of uncertainties in the constitutive elastic properties of material constituting a circular column under axial compression. To this aim, a probabilistic model dedicated to the construction of positive-definite random elasticity matrices was first used, [...] Read more.

This study is devoted to the modeling and simulation of uncertainties in the constitutive elastic properties of material constituting a circular column under axial compression. To this aim, a probabilistic model dedicated to the construction of positive-definite random elasticity matrices was first used, involving two stochastic parameters: the mean value and a dispersion parameter. In order to compute the nonlinear effects between load and lateral deflection for the buckling problem of the column, a finite element framework combining a Newton-Raphson solver was developed. The finite element tool was validated by comparing the as-obtained critical buckling loads with those from Euler’s formula at zero-fluctuation of the elasticity matrix. Three levels of fluctuations of material uncertainties were then propagated through the validated finite element tool using the probabilistic method as a stochastic solver. Results showed that uncertain material properties considerably influenced the buckling behavior of columns under axial loading. The coefficient of variation of a critical buckling load over 500 realizations were 15.477%, 26.713% and 41.555% when applying dispersion parameters of 0.3, 0.5 and 0.7, respectively. The 95% confidence intervals of column buckling response were finally given. The methodology of modeling presented in this paper is a potential candidate for accounting material uncertainties with some instabilities of structural elements under compression. Full article

(This article belongs to the Special Issue Randomness and Uncertainty)

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13 pages, 508 KiB

Open AccessArticle

Uncertainty Quantification for Ti-7Al Alloy Microstructure with an Inverse Analytical Model (AUQLin)

by Pınar Acar

Materials 2019, 12(11), 1773; https://doi.org/10.3390/ma12111773 - 31 May 2019

Cited by 18 | Viewed by 2570

Abstract

The present study addresses an inverse problem for observing the microstructural stochasticity given the variations in the macro-scale material properties by developing an analytical uncertainty quantification (UQ) model called AUQLin. The uncertainty in the material property is modeled with the analytical algorithm, and [...] Read more.

The present study addresses an inverse problem for observing the microstructural stochasticity given the variations in the macro-scale material properties by developing an analytical uncertainty quantification (UQ) model called AUQLin. The uncertainty in the material property is modeled with the analytical algorithm, and then the uncertainty propagation to the microstructure is solved with an inverse problem that utilizes the transformation of random variables principle. The inverse problem leads to an underdetermined linear system, and thus produces multiple solutions to the statistical features of the microstructure. The final solution is decided by solving an optimization problem which aims to minimize the difference between the computed and experimental statistical parameters of the microstructure. The final result for the computed microstructural uncertainty is found to provide a good match to the experimental microstructure information. Full article

(This article belongs to the Special Issue Randomness and Uncertainty)

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24 pages, 7023 KiB

Open AccessArticle

Adaptivity in Bayesian Inverse Finite Element Problems: Learning and Simultaneous Control of Discretisation and Sampling Errors

by Pierre Kerfriden, Abhishek Kundu and Susanne Claus

Materials 2019, 12(4), 642; https://doi.org/10.3390/ma12040642 - 20 Feb 2019

Cited by 2 | Viewed by 4565

Abstract

The local size of computational grids used in partial differential equation (PDE)-based probabilistic inverse problems can have a tremendous impact on the numerical results. As a consequence, numerical model identification procedures used in structural or material engineering may yield erroneous, mesh-dependent result. In [...] Read more.

The local size of computational grids used in partial differential equation (PDE)-based probabilistic inverse problems can have a tremendous impact on the numerical results. As a consequence, numerical model identification procedures used in structural or material engineering may yield erroneous, mesh-dependent result. In this work, we attempt to connect the field of adaptive methods for deterministic and forward probabilistic finite-element (FE) simulations and the field of FE-based Bayesian inference. In particular, our target setting is that of exact inference, whereby complex posterior distributions are to be sampled using advanced Markov Chain Monte Carlo (MCMC) algorithms. Our proposal is for the mesh refinement to be performed in a goal-oriented manner. We assume that we are interested in a finite subset of quantities of interest (QoI) such as a combination of latent uncertain parameters and/or quantities to be drawn from the posterior predictive distribution. Next, we evaluate the quality of an approximate inversion with respect to these quantities. This is done by running two chains in parallel: (i) the approximate chain and (ii) an enhanced chain whereby the approximate likelihood function is corrected using an efficient deterministic error estimate of the error introduced by the spatial discretisation of the PDE of interest. One particularly interesting feature of the proposed approach is that no user-defined tolerance is required for the quality of the QoIs, as opposed to the deterministic error estimation setting. This is because our trust in the model, and therefore a good measure for our requirement in terms of accuracy, is fully encoded in the prior. We merely need to ensure that the finite element approximation does not impact the posterior distributions of QoIs by a prohibitively large amount. We will also propose a technique to control the error introduced by the MCMC sampler, and demonstrate the validity of the combined mesh and algorithmic quality control strategy. Full article

(This article belongs to the Special Issue Randomness and Uncertainty)

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28 pages, 12727 KiB

Open AccessArticle

Stochastic Constitutive Model of Isotropic Thin Fiber Networks Based on Stochastic Volume Elements

by Rami Mansour, Artem Kulachenko, Wei Chen and Mårten Olsson

Materials 2019, 12(3), 538; https://doi.org/10.3390/ma12030538 - 11 Feb 2019

Cited by 31 | Viewed by 4853

Abstract

Thin fiber networks are widely represented in nature and can be found in man-made materials such as paper and packaging. The strength of such materials is an intricate subject due to inherited randomness and size-dependencies. Direct fiber-level numerical simulations can provide insights into [...] Read more.

Thin fiber networks are widely represented in nature and can be found in man-made materials such as paper and packaging. The strength of such materials is an intricate subject due to inherited randomness and size-dependencies. Direct fiber-level numerical simulations can provide insights into the role of the constitutive components of such networks, their morphology, and arrangements on the strength of the products made of them. However, direct mechanical simulation of randomly generated large and thin fiber networks is characterized by overwhelming computational costs. Herein, a stochastic constitutive model for predicting the random mechanical response of isotropic thin fiber networks of arbitrary size is presented. The model is based on stochastic volume elements (SVEs) with SVE size-specific deterministic and stochastic constitutive law parameters. The randomness in the network is described by the spatial fields of the uniaxial strain and strength to failure, formulated using multivariate kernel functions and approximate univariate probability density functions. The proposed stochastic continuum approach shows good agreement when compared to direct numerical simulation with respect to mechanical response. Furthermore, strain localization patterns matched the one observed in direct simulations, which suggests an accurate prediction of the failure location. This work demonstrates that the proposed stochastic constitutive model can be used to predict the response of random isotropic fiber networks of arbitrary size. Full article

(This article belongs to the Special Issue Randomness and Uncertainty)

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24 pages, 855 KiB

Open AccessArticle

A Mass Conservative Kalman Filter Algorithm for Computational Thermo-Fluid Dynamics

by Carolina Introini, Stefano Lorenzi, Antonio Cammi, Davide Baroli, Bernhard Peters and Stéphane Bordas

Materials 2018, 11(11), 2222; https://doi.org/10.3390/ma11112222 - 8 Nov 2018

Cited by 9 | Viewed by 5120

Abstract

This paper studies Kalman filtering applied to Reynolds-Averaged Navier–Stokes (RANS) equations for turbulent flow. The integration of the Kalman estimator is extended to an implicit segregated method and to the thermodynamic analysis of turbulent flow, adding a sub-stepping procedure that ensures mass conservation [...] Read more.

This paper studies Kalman filtering applied to Reynolds-Averaged Navier–Stokes (RANS) equations for turbulent flow. The integration of the Kalman estimator is extended to an implicit segregated method and to the thermodynamic analysis of turbulent flow, adding a sub-stepping procedure that ensures mass conservation at each time step and the compatibility among the unknowns involved. The accuracy of the algorithm is verified with respect to the heated lid-driven cavity benchmark, incorporating also temperature observations, comparing the augmented prediction of the Kalman filter with the Computational Fluid-Dynamic solution found on a fine grid. Full article

(This article belongs to the Special Issue Randomness and Uncertainty)

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17 pages, 4836 KiB

Open AccessArticle

Filling of Irregular Channels with Round Cross-Section: Modeling Aspects to Study the Properties of Porous Materials

by Yamel Ungson, Larysa Burtseva, Edwin R. Garcia-Curiel, Benjamin Valdez Salas, Brenda L. Flores-Rios, Frank Werner and Vitalii Petranovskii

Materials 2018, 11(10), 1901; https://doi.org/10.3390/ma11101901 - 5 Oct 2018

Cited by 7 | Viewed by 4441 | Correction

Abstract

The filling of channels in porous media with particles of a material can be interpreted in a first approximation as a packing of spheres in cylindrical recipients. Numerous studies on micro- and nanoscopic scales show that they are, as a rule, not ideal [...] Read more.

The filling of channels in porous media with particles of a material can be interpreted in a first approximation as a packing of spheres in cylindrical recipients. Numerous studies on micro- and nanoscopic scales show that they are, as a rule, not ideal cylinders. In this paper, the channels, which have an irregular shape and a circular cross-section, as well as the packing algorithms are investigated. Five patterns of channel shapes are detected to represent any irregular porous structures. A novel heuristic packing algorithm for monosized spheres and different irregularities is proposed. It begins with an initial configuration based on an fcc unit cell and the subsequent densification of the obtained structure by shaking and gravity procedures. A verification of the algorithm was carried out for nine sinusoidal axisymmetric channels with different D_min/D_max ratio by MATLAB^® simulations, reaching a packing fraction of at least 0.67 (for sphere diameters of 5%D_min or less), superior to a random close packing density. The maximum packing fraction was 73.01% for a channel with a ratio of D_min/D_max = 0.1 and a sphere size of 5%D_min. For sphere diameters of 50%D_min or larger, it was possible to increase the packing factor after applying shaking and gravity movements. Full article

(This article belongs to the Special Issue Randomness and Uncertainty)

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1 pages, 178 KiB

Open AccessCorrection

Correction: Ungson, Y. et al. Filling of Irregular Channels with Round Cross-Section: Modeling Aspects to Study the Properties of Porous Materials. Materials 2018, 11, 1901

by Yamel Ungson, Larysa Burtseva, Edwin R. Garcia-Curiel, Benjamin Valdez Salas, Brenda L. Flores-Rios, Frank Werner and Vitalii Petranovskii

Materials 2019, 12(5), 818; https://doi.org/10.3390/ma12050818 - 11 Mar 2019

Viewed by 2367

Abstract

The authors have found two errors in the paper published in Materials [...] Full article

(This article belongs to the Special Issue Randomness and Uncertainty)

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