Begell House Inc.
International Journal for Multiscale Computational Engineering
JMC
1543-1649
8
3
2010
SPECIAL ISSUE Multiscale Methods in Computer Materials Science
vii
Maciej
Pietrzyk
AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Kraków, Poland
P. D.
Hodgson
Centre for Material and Fibre Innovation, Deakin University, Geelong, Victoria 3217, Australia
Tadeusz
Burczynski
Institute of Fundamental Technological Research, Polish Academy of Sciences
A Multiscale Approach to Numerical Modeling of Solidification
251-257
Mariusz
Ciesielski
Institute of Matematics and Computer Science, Czestochowa University of Technology, 42-200 Czestochowa, Dabrowskiego 73, Poland
In this paper the multiscale approach to numerical modeling of solidification on the micro/macro level is presented. Two kinds of meshes are used. The casting domain is covered by the mesh of regular macrocells, and in every macrocell the mesh of control volumes is generated. The control volumes correspond to the final shape of grains and they are approximated by Thiessen polygons (a 2D task), while their central points correspond to the initial positions of nuclei (generated in a random way). The changes of the temporary volumetric fraction of solid at the considered point from the casting domain results from the laws determining the nucleation and nuclei growth. In order to solve the problem the control volume method is applied. In the final part of the paper an example of computation is shown.
Generalized Micro/Macro Model of Crystallization and Its Numerical Realization
259-266
Bohdan
Mochnacki
Czestochowa University of Technology, Dabrowskiego 69, 42-201 Czestochowa, Higher School of Labour Safety Management, Bankowa 8, 40-007 Katowice, Poland
Romuald
Szopa
Czestochowa University of Technology, 42-200 Czestochowa, Dabrowskiego 73, Poland
In this paper considerations concerning the mathematical micro/macro model of pure metals solidification are presented. A generalized approach close to the Mehl-Johnson-Avrami-Kolmogoroff theory is applied. The differential equation leading to the well-known linear and exponential models of crystallization is generalized by the introduction of an additional parameter n. In this way the power-type model is obtained (the linear and exponential models correspond to n = 0 and n = 1). On a stage of numerical simulation the course of nucleation and nuclei growth are simulated using the procedure based on the registration of successive grain family growth. Obtained in this way, the local capacities of internal heat sources are taken into account on a stage of solution corresponding to macroscale. A macro heat transfer is described by the Fourier-type equation. Finally, examples of numerical simulations and the results concerning the influence of model parameters on a course of solidification are shown.
Internal Variable and Cellular Automata-Finite Element Models of Heat Treatment
267-285
Piotr
Macioł
AGH-University of Science and Technology
Jerzy
Gawad
AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Krakow, Poland
Roman
Kuziak
Institute for Ferrous Metallurgy, K. Miarki Street 12-14, 44-100 Gliwice, Poland
Maciej
Pietrzyk
AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Kraków, Poland
A comparison of various approaches to modeling of phase transformations during heat treatment of steels is the objective of the paper. The first approach is a conventional model based on the Avrami-type equation. In this approach, the Avrami coefficients are introduced as the modified Gauss distribution function of temperature. This model is identified using inverse analysis applied to the dilatometric tests. The model with optimized parameters is implemented into the finite element code, which simulates heat treatment of steel parts. The second approach is a coupled finite element-cellular automata (CAFE) multiscale model, which accounts explicitly for the phenomena occurring during transformations in the microscale. Simulations using both models were performed and the results were compared. Advantages of the CAFE model, as far as predictive capabilities and efficiency are concerned, are presented in the final part of the paper.
A Multiscale Finite Element Approach for Buckling Analysis of Elastoplastic Long Fiber Composites
287-301
Saeid
Nezamabadi
Laboratoire de MÃ©canique et GÃ©nie Civil (LMGC), UMR 5508 CNRS
Hamid
Zahrouni
Universite Paul Verlaine de Metz, Laboratoire de Physique et Mecanique des Materiaux, FRE CNRS 3236, Ile du Saulcy 57045, Metz Cedex 01 France
Julien
Yvonnet
Universite Paris-Est, Laboratoire Modelisation et simulation Multi Echelle, 5 Bd Descartes, F-77454 Marne-la-Vallee Cedex 2, France
Michel
Potier-Ferry
Universite Paul Verlaine de Metz, Laboratoire de Physique et Mecanique des Materiaux, FRE CNRS 3236, Ile du Saulcy 57045, Metz Cedex 01 France
The present work is devoted to the microbuckling analysis of long fiber composites. A multiscale finite element method
(FE2) is combined with the asymptotic numerical method (ANM) to study the elastoplastic instability which may occur
in structures at both macroscopic and microscopic scales. The fiber is described by a linear material constitutive law,
while the matrix phase is described by a nonlinear Ramberg-Osgood relationship. The stress field is then obtained via
the total mechanical strain without any history dependence. Large strains are considered, which induce geometrical
nonlinearities in both cases. The ANM framework allows obtaining complex response curves involving limit points
in loading and displacement to be obtained. In the present path following procedure, adjustment of the step length is
naturally automatic because the validity range of the asymptotic solution is a posteriori estimated depending on the
local nonlinearity of the response branches. Numerical examples show the effectiveness of the proposed approach by
investigating microscopic and macroscopic instabilities of long fiber composite structures in compression.
Toward Two-Scale Adaptive FEM Modeling of Nonlinear Heterogeneous Materials
303-317
Marta
Serafin
Institute for Computational Civil Engineering, Cracow University of Technology, ul. Warszawska 24, 31-155 Krakow, Poland
Witold
Cecot
Institute for Computational Civil Engineering, Cracow University of Technology, ul. Warszawska 24, 31-155 Krakow, Poland
Two-scale modeling of periodic metal matrix composites reinforced with metallic inclusions is presented in this paper. The adaptive finite element method (FEM) is used to approximate solutions of elastic or inelastic problems at both levels in order to improve efficiency of computation. Mesh adaptation at the macroscale is more challenging, since each refinement introduces new representative volume elements for which the loading history is typically unknown but necessary for further computation. At the microscale, the mesh adaptation enables generation of the initial discretization independently of the material heterogeneity.
Molecular Statics Coupled with the Subregion Boundary Element Method in Multiscale Analysis
319-330
Tadeusz
Burczynski
Institute of Fundamental Technological Research, Polish Academy of Sciences
Adam
Mrozek
AGH University of Science and Technology, Cracow, Poland
Radoslaw
Gorski
Department for Strength of Materials and Computational Mechanics, Silesian University of Technology, Konarskiego 18a, 44-100 Gliwice, Poland
Waclaw
Kus
Department for Strength of Materials and Computational Mechanics, Silesian University of Technology, Konarskiego 18a, 44-100 Gliwice, Poland
This paper describes a numerical multiscale algorithm which couples two domains: a discrete atomistic domain and a continuum domain. The atomic model uses the Lennard-Jones and the Morse potentials, and the embedded atom method to compute interactions between atoms. The continuum domain and the interface area are modeled by the subregion boundary element method. Numerical tests are presented to examine the presented technique.
Continuum and Atomistic Modeling of the Mixed Straight Dislocation
331-342
Pawel
Dluzewski
Institute of Fundamental Technological Research, Polish Academy of Sciences, ul. Pawinskiego 5 B, 02-106 Warsaw, Poland
Toby D.
Young
Institute of Fundamental Technological Research, Polish Academy of Sciences, ul. Pawinskiego 5 B, 02-106 Warsaw, Poland
George P.
Dimitrakopulos
Department of Physics, Aristotle University of Thessaloniki, GR-54124 Thessaloniki, Greece
Philomela
Komninou
Department of Physics, Aristotle University of Thessaloniki, GR-54124 Thessaloniki, Greece
A continuum and atomistic approach to the modeling of dislocations observed by high-resolution transmission electron microscopy (HRTEM) is discussed in terms of the continuum theory of dislocations. The atomistic models are obtained by means of the use of a mathematical formula for discrete dislocations. A new analytical solution for a continuously distributed dislocation core is presented. This solution is employed in the finite element modeling of residual stresses induced by the net of dislocations visible on an HRTEM image of GaN structure. This paper terminates with some comments on the atomistic/finite-element modeling of dislocation fields. Because of some confusion concerning notations used in the literature, the mathematical foundations of the continuum theory of dislocations are revisited.
Application of the Automatic Image Processing in Modeling of the Deformation Mechanisms Based on the Digital Representation of Microstructure
343-356
Lukasz
Rauch
AGH University of Science and Technology, al. Mickiewicza 30, 30-059 Kraków, Poland
L.
Madej
AGH-University of Science and Technology, Al. Mickiewicza 30, 30-059 Krakow, Poland
Numerical modeling based on digital material representation (DMR) prepared on the basis of the automated multiscale processing of microstructure photographs is the subject of this work. The main assumptions of the proposed algorithms, including image filtering, reconstruction, and grain analysis of one- and two-phase materials, are described in the paper. Their advantages and limitations are also discussed in detail. Then the results of the image analysis in the form of explicitly described microstructure representation in two dimensions are passed as input data directly to the finite element software. The sample of digital material is analyzed in order to generate the mesh of finite elements and to attach necessary rheological models. These data are then used during finite element simulations of plastometric compression tests. Examples of obtained stress and strain distribution across an explicitly represented microstructure after deformation are presented and discussed. Directions for future development of the presented approach are also highlighted.