Translation random field with marginal beta distribution in modeling material properties

Structure material properties are heterogeneous in nature and would be characterized with different statistics at different length scales due to the spatially averaging effects. This work develops a framework for the modal analysis of beam structures with random field models at multiple scales. In this framework, the random field theory is adopted to model heterogeneous material properties, and the cross-correlations between material properties are explicitly considered. The modal parameters of a structure are then evaluated using the finite element (FE) method with the simulated heterogeneous material properties taken as input. With the aid of Monte Carlo simulation, the modal parameters are analyzed in a probabilistic manner. In addition, to accommodate the necessity of different mesh sizes in FE models, an approach of evaluating random field parameters and generating random field material properties at different length scales is developed. The performance of the proposed framework is demonstrated through the modal analysis of a simply supported beam, where the formulation of the multiscale random field approach is validated and the effects of heterogeneous material properties on modal parameters are analyzed. Parametric studies on the random field parameters, including the coefficient of variation and the scale of fluctuation, are also conducted to further investigate the relations between the random field parameters at different scales.

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Physics Based B-Spline Heterogeneous Object Modeling

Volume 1: 21st Computers and Information in Engineering Conference ◽

10.1115/detc2001/cie-21664 ◽

2001 ◽

Author(s):

Xiaoping Qian ◽

Debasish Dutta

Keyword(s):

Diffusion Process ◽

Material Properties ◽

Degrees Of Freedom ◽

Heterogeneous Material ◽

Critical Issue ◽

Material Composition ◽

B Spline ◽

Material Heterogeneity ◽

Heterogeneous Objects ◽

Modeling Material

Abstract The task of modeling material heterogeneity (composition variation) is a critical issue in the design and fabrication of heterogeneous objects. Existing methods cannot efficiently model the material heterogeneity, due to the formidable size of the degrees of freedom for the specification of heterogeneous objects. In this research, we provide an intuitive way to model the object heterogeneity by using only a few parameters. These parameters carry physical meanings, such as diffusion coefficients in the diffusion process. We use a B-spline representation to model heterogeneous objects and material properties. We use diffusion equations to generate heterogeneous material composition profile. We then use finite element techniques to solve the material composition equations for the diffusion process. Finally we extend this method to the direct manipulation of material properties in heterogeneous objects.

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Efficient Uncertainty Quantification for Biotransport in Tumors With Uncertain Material Properties

Volume 3: Biomedical and Biotechnology Engineering ◽

10.1115/imece2018-86216 ◽

2018 ◽

Author(s):

Alen Alexanderian ◽

William Reese ◽

Ralph C. Smith ◽

Meilin Yu

Keyword(s):

Porous Media ◽

Random Field ◽

Material Properties ◽

Pressure Field ◽

Input Parameter ◽

Gaussian Random Field ◽

Porous Media Flow ◽

Expansion Technique ◽

Low Dimensional ◽

Permeability Field

We consider modeling of single phase fluid flow in heterogeneous porous media governed by elliptic partial differential equations (PDEs) with random field coefficients. Our target application is biotransport in tumors with uncertain heterogeneous material properties. We numerically explore dimension reduction of the input parameter and model output. In the present work, the permeability field is modeled as a log-Gaussian random field, and its covariance function is specified. Uncertainties in permeability are then propagated into the pressure field through the elliptic PDE governing porous media flow. The covariance matrix of pressure is constructed via Monte Carlo sampling. The truncated Karhunen–Loève (KL) expansion technique is used to decompose the log-permeability field, as well as the random pressure field resulting from random permeability. We find that although very high-dimensional representation is needed to recover the permeability field when the correlation length is small, the pressure field is not sensitive to high-oder KL terms of input parameter, and itself can be modeled using a low-dimensional model. Thus a low-rank representation of the pressure field in a low-dimensional parameter space is constructed using the truncated KL expansion technique.

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An Efficient Method of Modeling Material Properties Using a Thermal Diffusion Analogy: An Example Based on Craniofacial Bone

PLoS ONE ◽

10.1371/journal.pone.0017004 ◽

2011 ◽

Vol 6 (2) ◽

pp. e17004 ◽

Cited By ~ 16

Author(s):

Julian L. Davis ◽

Elizabeth R. Dumont ◽

David S. Strait ◽

Ian R. Grosse

Keyword(s):

Thermal Diffusion ◽

Efficient Method ◽

Material Properties ◽

Craniofacial Bone ◽

Modeling Material

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Direct Simulation Methods for a Class of Normal and Lognormal Random Fields with Applications in Modeling Material Properties

Journal of Engineering Mechanics ◽

10.1061/(asce)em.1943-7889.0002076 ◽

2022 ◽

Vol 148 (2) ◽

Author(s):

Pei-Pei Fang ◽

Yong Liu ◽

Michael D. Shields

Keyword(s):

Material Properties ◽

Random Fields ◽

Simulation Methods ◽

Direct Simulation ◽

Lognormal Random Fields ◽

Modeling Material

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RANDOM FIELD GENERATION OF THE MATERIAL PROPERTIES IN A PERIDYNAMIC MODEL

10.26678/abcm.cobem2019.cob2019-0482 ◽

2019 ◽

Author(s):

Leandro Friedrich ◽

Mylena Barcellos da Silva ◽

Ignacio Iturrioz

Keyword(s):

Random Field ◽

Material Properties ◽

Field Generation ◽

Peridynamic Model ◽

Random Field Generation

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A patching algorithm for conditional random fields in modeling material properties

Computer Methods in Applied Mechanics and Engineering ◽

10.1016/j.cma.2021.113719 ◽

2021 ◽

Vol 377 ◽

pp. 113719

Author(s):

Jia-Yi Ou-Yang ◽

Dian-Qing Li ◽

Xiao-Song Tang ◽

Yong Liu

Keyword(s):

Material Properties ◽

Random Fields ◽

Conditional Random Fields ◽

Modeling Material

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Uncertainty Analysis for Biomechanical Injury of Cervical Spine Column

Volume 2: Biomedical and Biotechnology Engineering ◽

10.1115/imece2008-67857 ◽

2008 ◽

Cited By ~ 1

Author(s):

Taek Hyun Jang ◽

Stephen Ekwaro-Osire ◽

J. Brian Gill ◽

Javad Hashemi

Keyword(s):

Cervical Spine ◽

Random Field ◽

Material Properties ◽

Random Fields ◽

Random Variables ◽

Analysis Procedure ◽

Field Analysis ◽

Complex Structures ◽

Young’S Moduli ◽

Sensitive Parameters

Uncertain parameters exist in complex structures, such as the cervical spine, and they may produce unexpected significant influences on the structures. Therefore, for an accurate injury analysis of the cervical spine, it is essential to consider the uncertainties contained in the cervical spine components. For this research, motions segment of finite element C5-C6 motion segment was created and validated based on experimental data under various loading conditions. Young’s moduli of the cervical spine components were considered random variables. Then, based on the sensitivity analysis, Young’s moduli of the disc annulus and nucleus were considered random fields. Each random field was discretized into three and four sets of random variables for the disc annulus and nucleus, respectively. Using sets of random variables discretized from a random field, the sensitivities of the sensitive parameters were reduced to less than 0.05, in which the randomness may be ignored without losing analysis accuracy. The variance for probabilistic injury function was also decreased after random field analysis procedure. Moreover, considering material properties to be a random field, the reliability also increased. Reliability increased by 12.69% when Young’s modulus of both the disc annulus and nucleus were considered random fields.

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