Stochastic multiscale homogenization analysis of heterogeneous materials under finite deformations with full uncertainty in the microstructure

Ma, Ji; Sahraee, Shahab; Wriggers, Peter; Lorenzis, Laura De

doi:10.1007/s00466-015-1136-3

Cited by 39 publications

(18 citation statements)

References 30 publications

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“…3(a)) is used in the homogenization process. According to the homogenized results, the obtained thermal conductivity tensor has three different non-zero entries, κ Mii , (i = 1, 2, 3), therefore, the random vector V has totally 24 entries with V (1) , ..., V (21) relating to the random meso-scale elastic tensors C C C M and V (22) , V (23) and V (24) relating to the random meso-scale thermal conductivity tensors κ κ κ M (see Section 3.2.2).…”

Section: Random Vector Field Of Vmentioning

confidence: 99%

“…This last property of SVEs has been used to up-scale the uncertainties at the micro-scale to the meso-scale, for example to define the probability convergence criterion of RVE for masonry [10], to study the scale-dependency of homogenization for random composite materials [42], to obtain the property variations of poly-silicon film [25], to extract effective properties of random two-phase composites [39], or again to capture the stochastic properties of the parameters in a constitutive model [47]. The problem of finite elasticity was also considered through the resolution of composite material elementary cells in [4,24], which allows defining a meso-scale potential as proposed in [4].…”

Section: Introductionmentioning

confidence: 99%

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A stochastic multi-scale approach for the modeling of thermo-elastic damping in micro-resonators

Lucas

Nguyễn

et al. 2016

Computer Methods in Applied Mechanics and Engineering

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The aim of this work is to study the thermo-elastic quality factor (Q) of micro-resonators with a stochastic multi-scale approach. In the design of high-Q micro-resonators, thermo-elastic damping is one of the major dissipation mechanisms, which may have detrimental effects on the quality factor, and has to be predicted accurately. Since material uncertainties are inherent to and unavoidable in micro-electromechanical systems (MEMS), the effects of those variations have to be considered in the modeling in order to ensure the required MEMS performance. To this end, a coupled thermo-mechanical stochastic multi-scale approach is developed in this paper. Thermo-mechanical micro-models of polycrystalline materials are used to represent micro-structure realizations. A computational homogenization procedure is then applied on these statistical volume elements to obtain the stochastic characterizations of the elasticity tensor, thermal expansion, and conductivity tensors at the meso-scale. Spatially correlated meso-scale random fields can thus be generated to represent the stochastic behavior of the homogenized material properties. Finally, the distribution of the thermo-elastic quality factor of MEMS resonators is studied through a stochastic finite element method using as input the generated stochastic random field.

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Section: Random Vector Field Of Vmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A stochastic multi-scale approach for the modeling of thermo-elastic damping in micro-resonators

Lucas

Nguyễn

et al. 2016

Computer Methods in Applied Mechanics and Engineering

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“…In the paper there are involved the strain displacement relations, constitutive equations and differential equilibrium equations. There was used homogenization for calculating the material characteristics given in the example [17][18][19].…”

Section: Resultsmentioning

confidence: 99%

Laminate circular cylindrical shell

Kormaníková

Kotrasová

2017

MATEC Web Conf.

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The paper deals with a numerical approach of optimal design modelling of laminate circular cylindrical shell. For thin-walled shells the classical shell theory is capable of accurately predicting the shell behaviour. In the frame of numerical optimization of circular cylindrical shell there is made the minimization of weight subject to displacement constraint. Thickness of layers is taken as design variable. In the example there is found the thickness of the shell laminate roof under constant pressure loading using Modified Feasible Direction method.

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“…Different aspects and applications of stochastic computational homogenization were also reported in the literature …”

Section: Introductionmentioning

confidence: 99%

Fuzzy‐stochastic FEM–based homogenization framework for materials with polymorphic uncertainties in the microstructure

Pivovarov

Oberleiter

Willner

et al. 2018

Numerical Meth Engineering

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Summary Uncertainties in the macroscopic response of heterogeneous materials result from two sources: the natural variability in the microstructure's geometry and the lack of sufficient knowledge regarding the microstructure. The first type of uncertainty is denoted aleatoric uncertainty and may be characterized by a known probability density function. The second type of uncertainty is denoted epistemic uncertainty. This kind of uncertainty cannot be described using probabilistic methods. Models considering both sources of uncertainties are called polymorphic. In the case of polymorphic uncertainties, some combination of stochastic methods and fuzzy arithmetic should be used. Thus, in the current work, we examine a fuzzy‐stochastic finite element method–based homogenization framework for materials with random inclusion sizes. We analyze an experimental radii distribution of inclusions and develop a stochastic representative volume element. The stochastic finite element method is used to obtain the material response in the case of random inclusion radii. Due to unavoidable noise in experimental data, an insufficient number of samples, and limited accuracy of the fitting procedure, the radii distribution density cannot be obtained exactly; thus, it is described in terms of fuzzy location and scale parameters. The influence of fuzzy input on the homogenized stress measures is analyzed.

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Stochastic multiscale homogenization analysis of heterogeneous materials under finite deformations with full uncertainty in the microstructure

Cited by 39 publications

References 30 publications

A stochastic multi-scale approach for the modeling of thermo-elastic damping in micro-resonators

A stochastic multi-scale approach for the modeling of thermo-elastic damping in micro-resonators

Laminate circular cylindrical shell

Fuzzy‐stochastic FEM–based homogenization framework for materials with polymorphic uncertainties in the microstructure

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