Generation of dedicated finite element meshes for multiscale applications with delaunay triangulation and adaptive finite element cellular automata algorithms
Łukasz Madej1
, Filip Krużel2, Paweł Cybułka1, Konrad Perzyński1, Krzysztof Banaś1,2
1AGH University of Science and Technology, Kraków, Poland.
2Cracow University of Technology, Kraków, Poland.
DOI:
https://doi.org/10.7494/cmms.2012.2.0386
Abstract:
The main aim of the work is development and comparison of algorithms for mesh creation that can be further used to investigate material behavior under loading conditions, on the basis of digital material representation. Particular attention is put on development of conforming meshes for two-phase materials. Two approaches are investigated within the present work. The first is based on mesh refinement along particular microstructure features. The second incorporates the cellular automata phase transformation model into the finite element adaptation technique. Description of the two approaches and an example of application of the obtained meshes to analyze multiscale material behavior under plastic deformation condition are presented.
Cite as:
Madej, Ł., Krużel, F., Cybułka, P., Perzyński, K., & Banaś, K. (2012). Generation of dedicated finite element meshes for multiscale applications with delaunay triangulation and adaptive finite element cellular automata algorithms. Computer Methods in Materials Science, 12(2), 85 – 96. https://doi.org/10.7494/cmms.2012.2.0386
Article (PDF):
Keywords:
Finite element mesh generation, Digital material representation, Inhomogeneous deformation, Mesh refinement
References:
Beladi, H., Adachi, Y., Timokhina, I., Hodgson, P.D., 2009, Crystallographic analysis of nanobainitic steels, Scripta Materialia, 60, 455-458.
Bernacki, M, Chastel, Y, Digonnet, H, Resk, H, Coupez, T., Loge, RE, 2007, Development of numerical tools for the multiscale modelling of recrystallization in metals, based on a digital material framework, Computer Methods in Materials Science, 7, 141-149.
Bemacki, M., Chastel, Y., Coupez, T., Loge, R., 2008, Level set method for the numerical modelling of primary recrystallization in the polycrystalline materials, Scripta Materialia, 58, 12, 1129-1132.
Bernacki, M., Resk, H., Coupez, T., Loge, R.E., 2009, Finite element model of primary recrystallization in polycrystalline aggregates using a level set framework, Modelling and Simulation in Materials Science and Engineering, 17, 064006.
Brahme, A., Alvi, M.H., Saylor, D., Frify, J., Rollett, A.D., 2006, 3D reconstruction of microstructure in a commercial purity aluminum, Scripta Materialia, 55, 75-80.
Delannay, L., Jacques, P.J., Kalidini, S.R., 2006, Finte element modeling of crystal plasticity with grains shaped as trunced octahedrons, International Journal of Plasticity, 22, 1879-1898.
Gawad, J., Paszyński, M., Matuszyk, P., Madej, L., 2008, Cellular automata coupled with hp-adaptive Finite Element Method applied to simulation of austenite-ferrite phase transformation with a moving interface, Steel Research International, 79, 579-586.
Kurzydlowski, K.J., 2010, Modelling of the microstructure and properties in the length scales varying from nano- to macroscopic, Bulletin of the polish academy of sciences, Technical sciences, 58, 217-226.
Kuziak, R., Pidvysots’kyy, V., Weglarczyk, S., Pietrzyk, M., 2011, Bainitic steels as alternative for conventional carbon-manganese steels in manufacturing of fasteners -simulation of production chain, Computer Methods in Materials Science, 11, 443-462.
Loge R.E., Bernacki, M., Resk, H., Delannay, L., Digonnet, H., Chastel, Y., Coupez, T., 2008, Linking plastic deformation to recrystallization in metals, using digital micro-structures, Philosophical Magazine, 88, 3691-3712.
Madej L., Mrozek A., Kus W., Burczyński T., Pietrzyk M., 2008, Concurrent and upscaling methods in multi scale modelling – case studies Computer Methods in Materials Science, 8, 1-15.
Madej, L., Cybulka, G., Perzynski, K., Rauch, L., Pietrzyk, M., 2009, Multi-scale modeling based on Digital Material Representation, eds. E. Onate, D. R. J. Owen, B. Suarez, Proc. Conf, Complas 2009, Barcelona, CD.
Madej, L., 2010a, Digital material representation – new perspectives in numerical simulations of inhomogenous deformation, Computer Methods in Materials Science, 10, 143-155.
Madej, L., 2010b, Development of the modeling strategy for the strain localization simulation based on the Digital Material Representation, AGH University Press, Krakow. L., 2010c, Influence of microstructure features on strain distribution during micro forming on the basis of Digital Material Representation, Steel Research International, 81, 1438-1441.
Madej, L., Cybulka, P., Perzyński, K., Rauch, L., 2011a, Numerical analysis of strain inhomogeneities during deformation on the basis of the three dimensional Digital Material Representation, Computer Methods in Materials Science, 10, 375-380.
Madej, L., Rauch, L., Perzyński, K., Cybulka, P., 2011b, Digital Material Representation as an efficient tool for strain in-homogeneities analysis at the micro-scale level, Archives of Civil and Mechanical Engineering, 11, 661-679.
Madej, L., Szyndler, J., Pasternak, K., Przenzak, M., Rauch, L., 2011c, Tools for generation of digital material representations, Proc. Conf MS&T2011, Columbus, Ohio, CD.
Malinowski, Z., Głowacki, M., Pietrzyk, M., Madej, W., 2004, Finite element model for efficient simulation of ring rolling, Proc. Conf MS&T 2004, New Orleans, Louisiana USA, 397-401.
Pietrzyk, M., Madej, L, Rauch, L., Spytkowski, P., Kusiak, J., 2010, Conventional and multiscale modelling of austenite decomposition during laminar cooling of hot rolled DP steels, Proc. XXIX Verformungskundliches Kolloquium, Planeralm, 41-46.
Pietrzyk, M., Pidvysotskyy, V., Packo, M., 2004, Flow stress model accounting for the strain localization during plastic deformation of metals, Annals of the CIRP, 53, 235-238.
Rauch Ł., Madej Ł., 2010, Application of the automatic image processing in modeling of the deformation mechanisms based on the digital representation of microstructure, International Journal on Multi Scale Modeling, 8, 343-356.
Robertson, L.T., Hilditch, T.B., Hodgson, P.D., 2008, The effect of prestrain and bake hardening on the low-cycle fatigue properties of TRIP steel, International Journal of Fatigue, 30, 587-594.
Rollett, A.D., Saylor, D., Frid, J., El-Dasher, B.S., Barhme, A., Lee, S-B., Cornwell, C, Noack R, 2004, Modelling polycrystalline microstructures in 3D, Proc. Conf Numi-form, eds Ghosh, S., Castro, J.C., Lee, J.K., Columbus, 71-77.
Sabirov, I., Estrin, Y., Barnett, M.R., Timokhina, I., Hodgson P.D., 2008, Tensile deformation of an ultrafine-grained aluminium alloy: Micro shear banding and grain boundary sliding, Acta Materialia, 56, 2223-2230.
Saylor, D.M, Fridy, J., Bassem, S., El-Dasher, B.S., Kee-Youing, J., Rollett, A.D., 2004, Statistically representative three-dimensional microstructures based on orthogonal observation sections, Metallurgical and Materials Transaction A, 35A, 1969-1979.
Thomser, C, Uthaisangsuk, V., Bleck, W., 2009, Influence of marten-site distribution on the mechanical properties of dual phase steels: experiments and simulation, steel research international, 80, 582-587.
Timokhina, I.B., Hodgson, P.D., Ringer, S.P., Zheng, R.K., Pereloma, E.V., 2007, Precipitate characterisation of an advanced high-strength low-alloy (HSLA) steel using atom probe tomography, Scripta Materialia, 56, 601-604.
Zienkiewicz, O.C., Zhu, J.Z., 1992, The superconvergent patch recovery and a posteriori error estimates, International Journal for Numerical Methods in Engineering, 33. 1331-1382.
Zhang, P., Balint, D. S., Lin, J., 2011, An integrated scheme for crystal plasticity analysis: Virtual grain structure genera¬tion, Computational Material Science, in press