Begell House
International Journal for Multiscale Computational Engineering
International Journal for Multiscale Computational Engineering
1543-1649
12
5
2014
TWO-SCALE NUMERICAL HOMOGENIZATION OF THE CONSTITUTIVE PARAMETERS OF REACTIVE POWDER CONCRETE
The paper is concerned with the modeling of reactive powder concrete (RPC) by using the method of numerical homogenization. More specifically, a two-scale modeling approach and the finite element method are used. The behavior of a model of RPC on the macro scale is described on the basis of the phenomena occurring in the microstructure of the material. The applied approach makes it possible to take into account the microstructure of material as concerns the different mechanical properties of its constituents. The method does not require any knowledge of the constitutive equations at the macro level, which are determined implicitly by solving a boundary value problem for a representative volume element (RVE) of RPC on the micro level. In order to determine the constitutive equations on the macro scale it is necessary to know the layout of microstructure, the constitutive equations at the micro level, and their parameters. In this contribution the response of each of the concrete constituents (cement matrix, sand, crushed quartz) is assumed to be elastic. The microstructure of RPC concrete is randomly generated. A computer program for the two-scale homogenization of 2D disks has been developed and numerical results for micro and micromacro test problems are presented. Further studies of the considered problem, including also laboratory experiments, are under way.
Arkadiusz
Denisiewicz
Institute of Building Engineering, University of Zielona Gora, Licealna 9, 65-417 Zielona Gora, Poland
Mieczyslaw
Kuczma
Institute of Structural Engineering, Poznan University of Technology, Pl. Marii Sklodowskiej-Curie 5, 60-965 Poznan, Poland
361-374
NONLOCAL/COARSE-GRAINING HOMOGENIZATION OF LINEAR ELASTIC MEDIA WITH NON-SEPARATED SCALES USING LEAST-SQUARE POLYNOMIAL FILTERS
In this paper, a nonlocal computational method is proposed to construct a mesoscopic (coarse-grained) model of linear elastic heterogeneous materials in the case of nonseparated scales. The framework, introduced in our previous paper (Yvonnet and Bonnet, 2014), extends the classical homogenization framework by using low-pass filters operators instead of averaging operators, and Green's nonlocal functions instead of localization operators. In the present work, we introduce a filtering procedure based on least-square polynomial approximation to avoid the numerical drawbacks of Gaussian filters infinite domains. The complete associated homogenization scheme is described, as well as a numerical procedure based on finite elements to compute the different homogenized operators from a unit cell. The methodology is validated by analyzing both local and mesoscopic mechanical fields in structures where heterogeneities are of comparable size with respect to the loading characteristic fluctuation wavelength.
Julien
Yvonnet
Universite Paris-Est, Laboratoire Modelisation et simulation Multi Echelle, 5 Bd Descartes, F-77454 Marne-la-Vallee Cedex 2, France
Guy
Bonnet
Universite Paris-Est, Laboratoire Modelisation et simulation Multi Echelle, 5 Bd Descartes, F-77454 Marne-la-Vallee Cedex 2, France
375-395
NUMERICAL MODELING OF PHASE TRANSFORMATION IN DUAL PHASE (DP) STEEL AFTER HOT ROLLING AND LAMINAR COOLING
Continuous development of the automotive industry is associated with the search for construction materials that combine high strength with good plastic properties and which allow improvement of the process technology. DP steels meet the high requirements for materials currently used in the automotive industry. Production of DP steels is a very complex process requiring precise control of technological parameters during thermo-mechanical treatment. Design of these processes can be significantly improved by the numerical models of phase transformations occurring in the DP steels. The main aim of this work is multiscale modeling of the austenite decomposition into ferrite, bainite, and martensite in processes of laminar cooling. Partial differential diffusion equation of carbon diffusion is solved with a moving boundary (Stefan problem). The solution was performed in the real microstructure of austenite, which was obtained using the electron microscope image and digital material representation. The developed model based on finite element modeling (FEM) solution of a diffusion equation allows one to determine phase volume fractions, grain size, and carbon segregation before the front of transformation in fluctuating temperature conditions. Results of numerical simulations were used for development of the relationship between microstructure and mechanical properties of DP steel strips.
Monika
Pernach
AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Krakow, Poland
Krzysztof
Bzowski
AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Kraków, Poland
Maciej
Pietrzyk
AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Kraków, Poland
397-410
DISLOCATION CORE RECONSTRUCTION BASED ON FINITE DEFORMATION APPROACH AND ITS APPLICATION TO 4H-SiC CRYSTAL
A proper reconstruction of discrete crystal structure with defects is an important problem in dislocation theory. Currently, procedures for dislocation core reconstruction presented in the literature usually neglect configuration changes. The present paper discusses a new approach, which uses an iterative algorithm to determine an atomistic configuration of the dislocation core. The mathematical background is based on finite deformation theory, in which an iterative algorithm searches for the new atomic configuration corresponding to the actual atomic configuration of the deformed crystal. Its application to the reconstruction of 4H-SiC crystal affected by the system of four threading dislocations is presented as an example. Molecular statics calculations suggest a lower potential energy, as well as dislocation core energy, per-atom energy, and per-atom stresses for the structure reconstructed by use of the iterative algorithm against the classical solution based on the Love's equations.
Jan
Cholewinski
Department of Computational Science, Institute of Fundamental Technological Research, Polish Academy of Sciences, Pawinskiego 5b, 02-106 Warsaw, Poland
Marcin
Maździarz
Department of Computational Science, Institute of Fundamental Technological Research, Polish
Academy of Sciences, Pawinskiego 5B, 02-106 Warsaw, Poland
Grzegorz
Jurczak
Department of Computational Science, Institute of Fundamental Technological Research, Polish Academy of Sciences, Pawinskiego 5b, 02-106 Warsaw, Poland
Pawel
Dluzewski
Institute of Fundamental Technological Research, Polish Academy of Sciences, ul. Pawinskiego 5 B, 02-106 Warsaw, Poland
411-421
HOMOGENIZATION OF THE SPECTRAL EQUATION IN ONE DIMENSION
The asymptotic behavior of a one-dimensional spectral problem with periodic coefficient is addressed for high-frequency modes by a method of Bloch wave homogenization. The analysis leads to a spectral problem including both microscopic and macroscopic eigenmodes. Numerical simulation results are provided to corroborate the theory.
Thi Trang
Nguyen
FEMTO-ST Institute, Departement Temps-Frequence, 26 Chemin de l'Epitaphe, 25000 Besancon, France
Michel
Lenczner
FEMTO-ST, Departement Temps-Frequence, University of Franche-Comte, 26 Chemin de l'Epitaphe, 25030 Besancon Cedex, France
Matthieu
Brassart
Laboratoire de Mathematiques de Besancon, University of Franche-Comte, France
423-450
A REDUCED COMPUTATIONAL MODEL FOR PREDICTION OF ELECTRICAL RESISTANCE IN FIBROUS COMPOSITES
The effective conductivity of a fibrous composite is investigated using the Monte Carlo simulation scheme and the finite-element method. The conductive fibers are modeled as randomly distributed resistors in a nonconductive matrix. The gap elements are constructed between neighboring fibers to model the interfiber contact. The resistance of a gap element is defined as a function of the gap distance and the contact area. The quantitative analysis is performed on the basis of an equivalent resistor network, and the relationships between the overall conductivity and various geometric parameters such as the volume fraction, the fiber aspect ratio, the fiber orientation angle, the tunneling effect, and the fiber length distribution, have been studied. The key results such as the percolation thresholds have been validated by the data reported in the literature. Compared to the full three-dimensional simulations, the reduced model presented in this work is computationally more efficient and can be used in other applications as well.
Xiaobo
Guo
Department of Mechanical and Materials Engineering, University of Denver, Denver, Colorado 80208, USA
Yun-Bo
Yi
Department of Mechanical and Materials Engineering, University of Denver, Denver, Colorado 80208, USA
Maciej S.
Kumosa
Department of Mechanical and Materials Engineering, University of Denver, Denver, Colorado 80208, USA
451-463