Concurrent and upscaling methods in multi scale modelling - case studies

• Autorzy: Madej Ł. , Mrozek A. , Kuś W. , Burczyński T. , Pietrzyk M.

Warianty tytułu

PL

Hybrydowe i hierarchiczne modele analizy wieloskalowe j

• Języki publikacji: EN

Abstrakty

EN

Selected examples of applications of multi scale modeling in various areas of mechanics and materials science are presented in the paper. Advantages and disadvantages of these approaches are shown. Based on the literature review a classification of multi scale methods into two groups was pointed out. The first is upscaling group based on representative volume element. The second is concurrent group, where the method used to describe the fine scale is usually applied to a part of the whole domain of the solution. Detailed discussion of these two groups is based on the multi scale models developed by the Authors. The concurrent model is based on the combination of the molecular dynamic with the boundary element method and is applied to simulation of material failure. The upscaling model is called CAFE and is based on the combination of the cellular automata with the finite element method. Applications of this model to prediction strain localization in materials subjected to plastic deformation are also demonstrated in the paper.

PL

W pracy zaprezentowano dynamicznie rozwijające się nowe metody obliczeniowe do analizy wieloskalowej, umożliwiające opis zjawisk zachodzących w materiale, niemożliwych do przewidywania tradycyjnymi metodami modelowania. Dokonano klasyfikacji metod na dwie grupy różniące się sposobem podejścia do symulacji w różnych skalach oraz do interakcji między nimi. Pierwsza z nich to grupa metod hierarchicznych, która bazuje na reprezentatywnym elemencie objętości. Druga grupa to metody symulujące dane zjawisko w całej lub w części objętości badanego materiału równocześnie w kilku skalach. Przyjęto nazywać je metodami hybrydowymi odzwierciedlając współbieżne prowadzenie obliczeń różnymi metodami w przeciwieństwie do metod hierarchicznych, gdzie obliczenia prowadzone są w reprezentacyjnych elementach objętości. Opisano interesujące modele bazujące na połączeniu metod analizy mikro np. Automatów Komórkowych (ang. CA), Monte Carlo (ang. MC) czy Dynamiki Molekularnej (ang. MD) z metodami analizy makro np. Metodą Elementów Skończonych (ang. FE) czy też Metodą Elementów Brzegowych (ang. BE). Przykłady tworzenia i zastosowania modeli hierarchicznych i hybrydowych w zastosowaniu do symulacji zjawisk zachodzących w materiale podczas odkształcania przedstawiono bazując na połączeniu metod CA i FE oraz MD i BE.

Słowa kluczowe

EN

multi scale modelling; cellular automata; atomic models; fracture; strain localization; micro shear bands

• Wydawca: Wydawnictwa AGH
• Czasopismo: Computer Methods in Materials Science
• Rocznik: 2008
• Tom: Vol. 8, No. 1
• Strony: 1--15
• Opis fizyczny: Bibliogr. 56 poz., rys.

Twórcy

autor

Madej Ł.

autor

Mrozek A.

autor

Kuś W.

autor

Burczyński T.

autor

Pietrzyk M.

• Institute of Computer Modelling,Cracow University of Technology, Warszawska 24, 31-155 Kraków, Poland,

Bibliografia

• Abraham, F.F., Broughton, J.Q., Berstine, N., Kaxiras, E., 1998, Spanning the continuum to quantum length scales in a dynamic simulations of brittle fracture, Europhys. Lett. 44,783-787
• Allix. 0., 2006, Multiscale strategy for solving industrial problems, Comp. Meth. Appl. Sci., 6,107-126.
• Belytscho, T., Lochnert, S., Song, J.-H., 2007, Multiscale aggregating discontinuities (MAD): A metod for circumventing loss of Stability, Int. J. Num. Meth. Eng., 69, (in press).
• Burczynski, T., Mrozek, A. Kuś, W., 2007, A computational continuum-discrete model of materials, Bulletin of the Polish Academy of Sciences, 50, l, 85-89
• Burczynski, T., 1995, The Boundary Element Method in Mechanics, WNT, Warszawa.
• Cizek, P., 2002, Characteristics of shear bands in an austenitic stainless steel during hot deformation, Mat. Sci. Eng. A324, 214-218.
• Das, S., Palmiere, EJ., Howard, I.C., 2002, CAFE: a tool for modelling thermomechanical processes, Proc. Conf. Thermomech. Processing: Mechanics, Microstructure & Control, eds, Palmiere, E.J., Mahfouf, M., Pinna, C., Sheffield, 296-301.
• Das, S., Abbod, M.F., Zhu, Q., Palmiere, EJ., Howard, I.C., Linkens, D.A., 2007, A combined neuro fuzzy-cellular automata based material model for finite element simulation of plane strain compression, Comput. Mater. Sci., (in press)
• Daw, M.S., Basket, M.I., 1983, Semiempirical, quantum mechanical calculation of hydrogen embrittlement in metals, Phys. Rev. Lett. 50, 1285-1288
• De Borst, R., 2007, Challenges in computational materials science, multiple scales, multi-physics and evolving discontinuities, Computational Material Science, (in press).
• Demkowicz, L., Rachowicz, W., Devloo, P., 2002, A Fully Automatic hp-Adaptivity, J. of Scientific Computing, 17, 127-155.
• Dumett, M. A., Vassilevski, P., Woodward, C.S., 2002, A multigrid method for nonlinear unstructured finite element elliptic equations, SIAM J. on Scientific Computing, 1-19.
• Estrin, Y., 1996, Dislocation Density Related Constitutive Modelling, in: unified constitutive laws of plastic deformation, (eds), Krausz, A.S., Krausz, K., Academic Press.
• Gandin, C. A., Rappaz, M., 1994, A coupled finite element - cellular automaton model for the prediction of dendritic grain structures in solidification processes, Acta Metall., 42, 2233-2246.
• Gandin, C.A., Rappaz, M., 1996, 3D cellular automaton algorithm for the prediction of dendritic grain growth, Acta Metallurgica, 45, 2187-2195.
• Gawąd, J., Pietrzyk, M., 2007, Application of cafe coupled model to description of microstructure development during dynamic recrystallization, Archives of Metallurgy and Materials, 52, 257-266.
• Grosman, F., 1997, Application of the Flow Stress Function in Programmes for Computer Simulation of Plastic Working Processes, J. Mat. Proc. Technol., 64, 169-180.
• Hirt, G., Kopp, R., Hofmann, O., Franzke, M., Barton, G., 2007, Implementing a high accuracy Multi-Mesh Method for incremental Bulk Metal Forming, Ann. CIRP, 56, 313-316.
• Lan, Y.J., Li, D.Z., Li, Y.Y., 2004, Modeling austenite decomposition into ferrite at different cooling rate in low-carbon steel with cellular automaton method, Acta Materialia, 52, 1721-1729.
• Lan, Y.J., Xiao, N.M., Li, D.Z., Li, Y.Y., 2005, Mesoscale simulation of deformed austenite decomposition into ferrite by coupling a cellular automaton method with a crystal plasticity finite element model, Acta Materialia, 53,991-1003.
• Lee, P.D., Chirazi, A., Atwood, R.C., Wand, W., 2004, Multi scale modeling of solidification microstructures, including microsegregation and microporosity, in an Al-Si-Cu alloy, Mat. Sci. Eng. A, A365, 57-65.
• Khvastunkov M.S., Leggoe J.W., 2004, Adapting cellular automata to model failure in spatially heterogeneous ductile alloys, Scripta Mater. 51, 309-31
• Korbel, A., 1998, Structural and mechanical aspects of homogeneous and non-homogeneous deformation in solids, Courses and Lectures - No. 386, Springer, 21-98.
• Kumar, M., Sasikumar, R., Kesavan, Nair P., 1998, Competition between nucleation and early growth of ferrite from austenite-studies using cellular automaton simulation, Acta Metallurgica, 46, 6291-6303.
• Kundu, S., Dutta, M., Ganguly, S., Chandra, S., 2004, Prediction of phase transformation and microstructure in steel using cellular automation technique, Scripta Mater., 50, 891-895.
• Madej, Ł., Hodgson, P.D., Pietrzyk, M., 2006, Multi scale analysis of material behavior during deformation processes, in: Foundation of Materials Design, eds, Kurzydłowski, K.J., Major, B., Zięba, P., Publ. Research Signpost, Kerala, 17-46.
• Madej, Ł., Hodgson, P.D., Pietrzyk, M., 2007, Multi-scale rheological model for discontinuous phenomena in materials under deformation conditions, Computational Materials Science, 38, 685-691.
• Madej, Ł., Hodgson, P.D., Pietrzyk, M., 2007, Comparison of the strain distribution obtained from multi scale and conventional approaches to modelling extrusion, Solid State Phenomena, 129,25-30.
• Madej, Ł., Hodgson, P.D., Pietrzyk, M., 2007, The validation of a multiscale rheological model of discontinuous phenomena during metal rolling, Computational Materials Science, 41, 236-214.
• Mieche, C., 2003, Computational micro-to-macro transitions for discretized micro-structures of heterogeneous materials at finite strains based on the minimization of averaged incremental energy, Comp. Meth. Appl. Mech. Engrg., 192,559-591.
• Milenin, A., Muskalski, Z., 2007, The FEM simulation of cementite lamellas deformation in pearlitic colony during drawing of high carbon steels, Proc. Conf. Numiform 2007, eds, Cesar de Są, J.M.A., Santos, A,D., Porot, 1375-1380.
• Mishin, Y., Farkas, D., 1999, Interatomic potentials for monoatomic metals from experimental data and ab initio calculations., Physical Review, 59, 5, 3393-3407
• Missoum-Benziane, D., Ryckelynck, D., Chinesta, F., 2007, A new fully coupled two-scale modeling for mechanical problems involving microstructure: The95/5 technique, Comp. Meth. Appl. Mech. Eng., 196, 2325-2337.
• Mrozek, A., Kuś, W., Burczynski, T., 2006, Analisis of the Material Behaviour at the Nanoscale, Proc. 35th Solid Mechanics Conference, Kraków, 283-284.
• Mrozek, A., Kuś, W., Burczynski, T., 2007, Application of the coupled boundary element method with atomic model in the static analysis, Computer Methods in Materials Science, 7, 284-288.
• Nemat-Nasser, S., 1999, Averaging theorems in finite deformation plasticity, Mech. Mater. 31, 493-523.
• Paszyński, M., Kurtz, J., Demkowicz, L., 2006, Parallel fully automatic hp-adaptive 2D finite element package, Comp. Meth. Appl. Mech. Eng.,195, 711-741.
• Pietrzyk, M., 1990, Finite element based model of structure development in the hot rolling process, Steel Research, 61,603-607.
• Pietrzyk, M., Madej, Ł., Szeliga, D., Kuziak, R., Pidvysotskyy, V., Paul, H., Wajda, W., 2006, Rheological Models of Metallic Materials, Research in Polish Metallurgy at the Beginning of XXI Century, ed., Świątkowski, K., Komitet Metalurgii PAN, Kraków, 325-346.
• Quested, T.E., Greer, A.L., 2005, Grain refinement of Al alloys: Micromechanisms determining as-cast grain size in directional solidification, Acta Mater., 53, 4643-4653.
• Rondanini, M., Barbato, A., Cavalloti, C., 2006, A multi scale model of the Si CVD process, Proc. Conf, MMM, Freiburg,98-101.
• Roucoules, C., Pietrzyk, M., Hodgson, P.D., 2003, Analysis of work hardening and recrystallization during the hot working of steel using a statistically based internal variable method, Mat. Sci. Eng., A339, 1-9.
• Sfantos G.K., Alibadi M.H., Multi-scale boundary element modeling of material degradation and fracture, Computer methods in applied mechanics and engineering, 196, 2007, 1310-1329.
• Shterenlikht, A, Howard, IC, 2006, The CAFE model of fracture - application to a TMCR steel, J. Fatigue and Fracture of Engineering Materials and Structures, 29, 770 -787.
• Sunyk, R., Steinmann, P, 2002, On higher gradients in continuum-atomistic modelling, Int. J. of Solids and Structures , 40, 6877-6896,
• Szeliga, D., Gawąd, J., Pietrzyk, M., 2006, Inverse analysis for identification of rheological and friction models in metal forming, Comp. Meth. Appl Mech. Engrg., 195, 6778-6798.
• Tadmor, E.B., Oritz, M., Philips, R., 1996, Quasicontinuum analysis in crystals, Phil Mag., A 73, 1529-1563
• Takatani, H., Gandin, Ch.A., Rappaz, M., 2000, EBSD characterization and modelling of columnar dendritic grains growing in the presence of fluid flow, Acta Materialia, 48, 675-688.
• Thevoz, Ph., Gandin, Ch.A., 2001, Micro-macroscopic solidification models, Encyclopedia of Materials: Science and Technology, Elsevier, 5637-5642.
• Vandyoussefi, M., Greer, A.L., 2002, Application of the cellular automata-finite element model to the grain refinement of directionally solidified 11-4.15 wt% Mg alloys, Acta Mater., 50, 1693-1705.
• Van Houte, P., Kanjarla, A.K., Val Bael, A., Seefeldt, M., Delannay, L., 2006, Multiscale modelling of the plastic anisotropy and deformation texture of polycrystaline materials, Eur. J. Mech. A-solid, 25, 634-648.
• Volker, J., Songul, K., Kaya, L., 2006, A two-level variational multiscale method for convection-dominated convection-diffusion equations, Comp. Meth. Appl. Mech. Eng., 195,4594-4603.
• Yang, X.L., Dong, H.B., Wang, W., Lee, P.D., 2004, Microscale simulation of stray grain formation in investment cast turbine blades, Matl Sci. Eng. A, A 386, 129-139.
• Yazdipour, N., Davis, C.H.J., Hodgson P.D., 2007, Simulation of dynamic recrystalization using random grid cellular automata, Computer Methods in Materials Science, 7,168-174.
• Yu, Q., Esche, S.K., 2005, A multi-scale approach for micro-structure prediction in thermo-mechanical processing of metals, J. Mater. Proc. Tech., 169, 493-502.
• Zhang, L., Zhang, C.B., Wang, Y.M., Wang, S.Q., Ye H.Q., 2003, A cellular automaton investigation of the trans-formation from austenite to ferrite during continuous cooling, Acta Materialia, 51, 5519-5527.